\documentclass[12pt,titlepage]{article}

\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{color}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
\usepackage{xparse}
\usepackage{hyperref}

%----Macros----------
%
% Unresolved issues:
%
%  \righttoleftarrow
%  \lefttorightarrow
%
%  \color{} with HTML colorspec
%  \bgcolor
%  \array with options (without options, it's equivalent to the matrix environment)

% Of the standard HTML named colors, white, black, red, green, blue and yellow
% are predefined in the color package. Here are the rest.
\definecolor{aqua}{rgb}{0, 1.0, 1.0}
\definecolor{fuschia}{rgb}{1.0, 0, 1.0}
\definecolor{gray}{rgb}{0.502, 0.502, 0.502}
\definecolor{lime}{rgb}{0, 1.0, 0}
\definecolor{maroon}{rgb}{0.502, 0, 0}
\definecolor{navy}{rgb}{0, 0, 0.502}
\definecolor{olive}{rgb}{0.502, 0.502, 0}
\definecolor{purple}{rgb}{0.502, 0, 0.502}
\definecolor{silver}{rgb}{0.753, 0.753, 0.753}
\definecolor{teal}{rgb}{0, 0.502, 0.502}

% Because of conflicts, \space and \mathop are converted to
% \itexspace and \operatorname during preprocessing.

% itex: \space{ht}{dp}{wd}
%
% Height and baseline depth measurements are in units of tenths of an ex while
% the width is measured in tenths of an em.
\makeatletter
\newdimen\itex@wd%
\newdimen\itex@dp%
\newdimen\itex@thd%
\def\itexspace#1#2#3{\itex@wd=#3em%
\itex@wd=0.1\itex@wd%
\itex@dp=#2ex%
\itex@dp=0.1\itex@dp%
\itex@thd=#1ex%
\itex@thd=0.1\itex@thd%
\advance\itex@thd\the\itex@dp%
\makebox[\the\itex@wd]{\rule[-\the\itex@dp]{0cm}{\the\itex@thd}}}
\makeatother

% \tensor and \multiscript
\makeatletter
\newif\if@sup
\newtoks\@sups
\def\append@sup#1{\edef\act{\noexpand\@sups={\the\@sups #1}}\act}%
\def\reset@sup{\@supfalse\@sups={}}%
\def\mk@scripts#1#2{\if #2/ \if@sup ^{\the\@sups}\fi \else%
  \ifx #1_ \if@sup ^{\the\@sups}\reset@sup \fi {}_{#2}%
  \else \append@sup#2 \@suptrue \fi%
  \expandafter\mk@scripts\fi}
\def\tensor#1#2{\reset@sup#1\mk@scripts#2_/}
\def\multiscripts#1#2#3{\reset@sup{}\mk@scripts#1_/#2%
  \reset@sup\mk@scripts#3_/}
\makeatother

% \slash
\makeatletter
\newbox\slashbox \setbox\slashbox=\hbox{$/$}
\def\itex@pslash#1{\setbox\@tempboxa=\hbox{$#1$}
  \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa
  \copy\slashbox \kern-\@tempdima \box\@tempboxa}
\def\slash{\protect\itex@pslash}
\makeatother

% math-mode versions of \rlap, etc
% from Alexander Perlis, "A complement to \smash, \llap, and lap"
%   http://math.arizona.edu/~aprl/publications/mathclap/
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathllap{\mathpalette\mathllapinternal}
\def\mathrlap{\mathpalette\mathrlapinternal}
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}
\def\mathclapinternal#1#2{\clap{$\mathsurround=0pt#1{#2}$}}

% Renames \sqrt as \oldsqrt and redefine root to result in \sqrt[#1]{#2}
\let\oldroot\root
\def\root#1#2{\oldroot #1 \of{#2}}
\renewcommand{\sqrt}[2][]{\oldroot #1 \of{#2}}

% Manually declare the txfonts symbolsC font
\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\SetSymbolFont{symbolsC}{bold}{U}{txsyc}{bx}{n}
\DeclareFontSubstitution{U}{txsyc}{m}{n}

% Manually declare the stmaryrd font
\DeclareSymbolFont{stmry}{U}{stmry}{m}{n}
\SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n}

% Manually declare the MnSymbolE font
\DeclareFontFamily{OMX}{MnSymbolE}{}
\DeclareSymbolFont{mnomx}{OMX}{MnSymbolE}{m}{n}
\SetSymbolFont{mnomx}{bold}{OMX}{MnSymbolE}{b}{n}
\DeclareFontShape{OMX}{MnSymbolE}{m}{n}{
    <-6>  MnSymbolE5
   <6-7>  MnSymbolE6
   <7-8>  MnSymbolE7
   <8-9>  MnSymbolE8
   <9-10> MnSymbolE9
  <10-12> MnSymbolE10
  <12->   MnSymbolE12}{}

% Declare specific arrows from txfonts without loading the full package
\makeatletter
\def\re@DeclareMathSymbol#1#2#3#4{%
    \let#1=\undefined
    \DeclareMathSymbol{#1}{#2}{#3}{#4}}
\re@DeclareMathSymbol{\neArrow}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\neArr}{\mathrel}{symbolsC}{116}
\re@DeclareMathSymbol{\seArrow}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\seArr}{\mathrel}{symbolsC}{117}
\re@DeclareMathSymbol{\nwArrow}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\nwArr}{\mathrel}{symbolsC}{118}
\re@DeclareMathSymbol{\swArrow}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\swArr}{\mathrel}{symbolsC}{119}
\re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46}
\re@DeclareMathSymbol{\Perp}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\Vbar}{\mathrel}{symbolsC}{121}
\re@DeclareMathSymbol{\sslash}{\mathrel}{stmry}{12}
\re@DeclareMathSymbol{\bigsqcap}{\mathop}{stmry}{"64}
\re@DeclareMathSymbol{\biginterleave}{\mathop}{stmry}{"6}
\re@DeclareMathSymbol{\invamp}{\mathrel}{symbolsC}{77}
\re@DeclareMathSymbol{\parr}{\mathrel}{symbolsC}{77}
\makeatother

% \llangle, \rrangle, \lmoustache and \rmoustache from MnSymbolE
\makeatletter
\def\Decl@Mn@Delim#1#2#3#4{%
  \if\relax\noexpand#1%
    \let#1\undefined
  \fi
  \DeclareMathDelimiter{#1}{#2}{#3}{#4}{#3}{#4}}
\def\Decl@Mn@Open#1#2#3{\Decl@Mn@Delim{#1}{\mathopen}{#2}{#3}}
\def\Decl@Mn@Close#1#2#3{\Decl@Mn@Delim{#1}{\mathclose}{#2}{#3}}
\Decl@Mn@Open{\llangle}{mnomx}{'164}
\Decl@Mn@Close{\rrangle}{mnomx}{'171}
\Decl@Mn@Open{\lmoustache}{mnomx}{'245}
\Decl@Mn@Close{\rmoustache}{mnomx}{'244}
\makeatother

% Widecheck
\makeatletter
\DeclareRobustCommand\widecheck[1]{{\mathpalette\@widecheck{#1}}}
\def\@widecheck#1#2{%
    \setbox\z@\hbox{\m@th$#1#2$}%
    \setbox\tw@\hbox{\m@th$#1%
       \widehat{%
          \vrule\@width\z@\@height\ht\z@
          \vrule\@height\z@\@width\wd\z@}$}%
    \dp\tw@-\ht\z@
    \@tempdima\ht\z@ \advance\@tempdima2\ht\tw@ \divide\@tempdima\thr@@
    \setbox\tw@\hbox{%
       \raise\@tempdima\hbox{\scalebox{1}[-1]{\lower\@tempdima\box
\tw@}}}%
    {\ooalign{\box\tw@ \cr \box\z@}}}
\makeatother

% \mathraisebox{voffset}[height][depth]{something}
\makeatletter
\NewDocumentCommand\mathraisebox{moom}{%
\IfNoValueTF{#2}{\def\@temp##1##2{\raisebox{#1}{$\m@th##1##2$}}}{%
\IfNoValueTF{#3}{\def\@temp##1##2{\raisebox{#1}[#2]{$\m@th##1##2$}}%
}{\def\@temp##1##2{\raisebox{#1}[#2][#3]{$\m@th##1##2$}}}}%
\mathpalette\@temp{#4}}
\makeatletter

% udots (taken from yhmath)
\makeatletter
\def\udots{\mathinner{\mkern2mu\raise\p@\hbox{.}
\mkern2mu\raise4\p@\hbox{.}\mkern1mu
\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}}
\makeatother

%% Fix array
\newcommand{\itexarray}[1]{\begin{matrix}#1\end{matrix}}
%% \itexnum is a noop
\newcommand{\itexnum}[1]{#1}

%% Renaming existing commands
\newcommand{\underoverset}[3]{\underset{#1}{\overset{#2}{#3}}}
\newcommand{\widevec}{\overrightarrow}
\newcommand{\darr}{\downarrow}
\newcommand{\nearr}{\nearrow}
\newcommand{\nwarr}{\nwarrow}
\newcommand{\searr}{\searrow}
\newcommand{\swarr}{\swarrow}
\newcommand{\curvearrowbotright}{\curvearrowright}
\newcommand{\uparr}{\uparrow}
\newcommand{\downuparrow}{\updownarrow}
\newcommand{\duparr}{\updownarrow}
\newcommand{\updarr}{\updownarrow}
\newcommand{\gt}{>}
\newcommand{\lt}{<}
\newcommand{\map}{\mapsto}
\newcommand{\embedsin}{\hookrightarrow}
\newcommand{\Alpha}{A}
\newcommand{\Beta}{B}
\newcommand{\Zeta}{Z}
\newcommand{\Eta}{H}
\newcommand{\Iota}{I}
\newcommand{\Kappa}{K}
\newcommand{\Mu}{M}
\newcommand{\Nu}{N}
\newcommand{\Rho}{P}
\newcommand{\Tau}{T}
\newcommand{\Upsi}{\Upsilon}
\newcommand{\omicron}{o}
\newcommand{\lang}{\langle}
\newcommand{\rang}{\rangle}
\newcommand{\Union}{\bigcup}
\newcommand{\Intersection}{\bigcap}
\newcommand{\Oplus}{\bigoplus}
\newcommand{\Otimes}{\bigotimes}
\newcommand{\Wedge}{\bigwedge}
\newcommand{\Vee}{\bigvee}
\newcommand{\coproduct}{\coprod}
\newcommand{\product}{\prod}
\newcommand{\closure}{\overline}
\newcommand{\integral}{\int}
\newcommand{\doubleintegral}{\iint}
\newcommand{\tripleintegral}{\iiint}
\newcommand{\quadrupleintegral}{\iiiint}
\newcommand{\conint}{\oint}
\newcommand{\contourintegral}{\oint}
\newcommand{\infinity}{\infty}
\newcommand{\bottom}{\bot}
\newcommand{\minusb}{\boxminus}
\newcommand{\plusb}{\boxplus}
\newcommand{\timesb}{\boxtimes}
\newcommand{\intersection}{\cap}
\newcommand{\union}{\cup}
\newcommand{\Del}{\nabla}
\newcommand{\odash}{\circleddash}
\newcommand{\negspace}{\!}
\newcommand{\widebar}{\overline}
\newcommand{\textsize}{\normalsize}
\renewcommand{\scriptsize}{\scriptstyle}
\newcommand{\scriptscriptsize}{\scriptscriptstyle}
\newcommand{\mathfr}{\mathfrak}
\newcommand{\statusline}[2]{#2}
\newcommand{\tooltip}[2]{#2}
\newcommand{\toggle}[2]{#2}

% Theorem Environments
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem*{utheorem}{Theorem}
\newtheorem*{ulemma}{Lemma}
\newtheorem*{uprop}{Proposition}
\newtheorem*{ucor}{Corollary}
\theoremstyle{definition}
\newtheorem{defn}{Definition}
\newtheorem{example}{Example}
\newtheorem*{udefn}{Definition}
\newtheorem*{uexample}{Example}
\theoremstyle{remark}
\newtheorem{remark}{Remark}
\newtheorem{note}{Note}
\newtheorem*{uremark}{Remark}
\newtheorem*{unote}{Note}

%-------------------------------------------------------------------

\begin{document}

%-------------------------------------------------------------------


\section*{Higher Algebra}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{higher_algebra}{}\paragraph*{{Higher algebra}}\label{higher_algebra}

[[!include higher algebra - contents]]

This entry collects links related to the book

\begin{itemize}%
\item [[Jacob Lurie]], \emph{Higher Algebra} (\href{http://www.math.harvard.edu/~lurie/papers/HA.pdf}{pdf})

\end{itemize}
on [[higher algebra]].

This book lays the basis of [[categorical algebra]] -- the study of the trinity [[Lawvere theory|algebra]], [[monads]], [[operads]] -- in the context of [[(∞,1)-category theory]]: [[(∞,1)-algebraic theory|(∞,1)-algebras]], [[(∞,1)-monad]]s, [[(∞,1)-operad]]s.

In particular it discusses the analogs of [[abelian groups]] and [[commutative rings]], namely [[abelian ∞-groups]], [[spectra]] and [[E-∞ rings]].

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{1_stable_categories}{1. Stable $\infty$-categories}\dotfill \pageref*{1_stable_categories} \linebreak
\noindent\hyperlink{11_foundations}{1.1 Foundations}\dotfill \pageref*{11_foundations} \linebreak
\noindent\hyperlink{111_stability}{1.1.1 Stability}\dotfill \pageref*{111_stability} \linebreak
\noindent\hyperlink{112_the_homotopy_category_of_a_stable_category}{1.1.2 The homotopy category of a stable $\infty$-category}\dotfill \pageref*{112_the_homotopy_category_of_a_stable_category} \linebreak
\noindent\hyperlink{113_closure_properties_of_stable_categories}{1.1.3 Closure properties of stable $\infty$-categories}\dotfill \pageref*{113_closure_properties_of_stable_categories} \linebreak
\noindent\hyperlink{114_exact_functors}{1.1.4 Exact functors}\dotfill \pageref*{114_exact_functors} \linebreak
\noindent\hyperlink{12_stable_categories_and_homological_algebra}{1.2 Stable $\infty$-categories and homological algebra}\dotfill \pageref*{12_stable_categories_and_homological_algebra} \linebreak
\noindent\hyperlink{121_tstructures_on_stable_categories}{1.2.1 t-Structures on stable $\infty$-categories}\dotfill \pageref*{121_tstructures_on_stable_categories} \linebreak
\noindent\hyperlink{122_filtered_objects_and_spectral_sequences}{1.2.2 Filtered objects and spectral sequences}\dotfill \pageref*{122_filtered_objects_and_spectral_sequences} \linebreak
\noindent\hyperlink{123_the_doldkan_correspondence}{1.2.3 The Dold-Kan correspondence}\dotfill \pageref*{123_the_doldkan_correspondence} \linebreak
\noindent\hyperlink{124_the_categorical_doldkan_correspondence}{1.2.4 The $\infty$-categorical Dold-Kan correspondence}\dotfill \pageref*{124_the_categorical_doldkan_correspondence} \linebreak
\noindent\hyperlink{13_homological_algebra_and_derived_categories}{1.3 Homological algebra and derived categories}\dotfill \pageref*{13_homological_algebra_and_derived_categories} \linebreak
\noindent\hyperlink{131_nerves_of_differential_graded_categories}{1.3.1 Nerves of differential graded categories}\dotfill \pageref*{131_nerves_of_differential_graded_categories} \linebreak
\noindent\hyperlink{132_derived_categories}{1.3.2 Derived $\infty$-categories}\dotfill \pageref*{132_derived_categories} \linebreak
\noindent\hyperlink{133_the_universal_property_of_}{1.3.3 The universal property of $\mathcal{D}^-(\mathcal{A})$}\dotfill \pageref*{133_the_universal_property_of_} \linebreak
\noindent\hyperlink{134_inverting_quasiisomorphisms}{1.3.4 Inverting Quasi-isomorphisms}\dotfill \pageref*{134_inverting_quasiisomorphisms} \linebreak
\noindent\hyperlink{135_grothendieck_abelian_categories}{1.3.5 Grothendieck abelian categories}\dotfill \pageref*{135_grothendieck_abelian_categories} \linebreak
\noindent\hyperlink{136_complexes_of_injective_objects}{1.3.6 Complexes of injective objects}\dotfill \pageref*{136_complexes_of_injective_objects} \linebreak
\noindent\hyperlink{14_spectra_and_stabilization}{1.4 Spectra and stabilization}\dotfill \pageref*{14_spectra_and_stabilization} \linebreak
\noindent\hyperlink{141_the_brown_representability_theorem}{1.4.1 The Brown representability theorem}\dotfill \pageref*{141_the_brown_representability_theorem} \linebreak
\noindent\hyperlink{142_spectrum_objects}{1.4.2 Spectrum objects}\dotfill \pageref*{142_spectrum_objects} \linebreak
\noindent\hyperlink{143_the_category_of_spectra}{1.4.3 The $\infty$-category of spectra}\dotfill \pageref*{143_the_category_of_spectra} \linebreak
\noindent\hyperlink{144_presentable_stable_categories}{1.4.4 Presentable stable $\infty$-categories}\dotfill \pageref*{144_presentable_stable_categories} \linebreak
\noindent\hyperlink{2_operads}{2. $\infty$-Operads}\dotfill \pageref*{2_operads} \linebreak
\noindent\hyperlink{21_foundations}{2.1 Foundations}\dotfill \pageref*{21_foundations} \linebreak
\noindent\hyperlink{211_from_colored_operads_to_operads}{2.1.1 From colored operads to $\infty$-operads}\dotfill \pageref*{211_from_colored_operads_to_operads} \linebreak
\noindent\hyperlink{212_maps_of_operads}{2.1.2 Maps of $\infty$-operads}\dotfill \pageref*{212_maps_of_operads} \linebreak
\noindent\hyperlink{213_algebra_objects}{2.1.3 Algebra objects}\dotfill \pageref*{213_algebra_objects} \linebreak
\noindent\hyperlink{214_preoperads}{2.1.4 $\infty$-Preoperads}\dotfill \pageref*{214_preoperads} \linebreak
\noindent\hyperlink{22_constructions_of_operads}{2.2 Constructions of $\infty$-Operads}\dotfill \pageref*{22_constructions_of_operads} \linebreak
\noindent\hyperlink{23_disintegration_and_assembly}{2.3 Disintegration and assembly}\dotfill \pageref*{23_disintegration_and_assembly} \linebreak
\noindent\hyperlink{231_disintegration_and_assembly}{2.3.1 Disintegration and assembly}\dotfill \pageref*{231_disintegration_and_assembly} \linebreak
\noindent\hyperlink{232_generalized_operads}{2.3.2 Generalized $\infty$-operads}\dotfill \pageref*{232_generalized_operads} \linebreak
\noindent\hyperlink{233_approximations_to_operads}{2.3.3 Approximations to $\infty$-operads}\dotfill \pageref*{233_approximations_to_operads} \linebreak
\noindent\hyperlink{234_disintegration_of_operads}{2.3.4 Disintegration of $\infty$-operads}\dotfill \pageref*{234_disintegration_of_operads} \linebreak
\noindent\hyperlink{24_products_and_coproducts}{2.4 Products and coproducts}\dotfill \pageref*{24_products_and_coproducts} \linebreak
\noindent\hyperlink{241_cartesian_symmetric_monoidal_structure}{2.4.1 Cartesian symmetric monoidal structure}\dotfill \pageref*{241_cartesian_symmetric_monoidal_structure} \linebreak
\noindent\hyperlink{242_monoid_objects}{2.4.2 Monoid objects}\dotfill \pageref*{242_monoid_objects} \linebreak
\noindent\hyperlink{243_cocartesian_symmetric_monoidal_structure}{2.4.3 CoCartesian Symmetric Monoidal Structure}\dotfill \pageref*{243_cocartesian_symmetric_monoidal_structure} \linebreak
\noindent\hyperlink{244_wreath_products}{2.4.4 Wreath Products}\dotfill \pageref*{244_wreath_products} \linebreak
\noindent\hyperlink{3_algebras_and_modules_over_operads}{3. Algebras and modules over $\infty$-operads}\dotfill \pageref*{3_algebras_and_modules_over_operads} \linebreak
\noindent\hyperlink{31_free_algebras}{3.1 Free algebras}\dotfill \pageref*{31_free_algebras} \linebreak
\noindent\hyperlink{32_limits_and_colimits_of_algebras}{3.2 Limits and colimits of algebras}\dotfill \pageref*{32_limits_and_colimits_of_algebras} \linebreak
\noindent\hyperlink{33_modules_over_operads}{3.3 Modules over $\infty$-operads}\dotfill \pageref*{33_modules_over_operads} \linebreak
\noindent\hyperlink{331_coherent_operads}{3.3.1 Coherent $\infty$-operads}\dotfill \pageref*{331_coherent_operads} \linebreak
\noindent\hyperlink{34_general_features_of_module_categories}{3.4 General features of module $\infty$-categories}\dotfill \pageref*{34_general_features_of_module_categories} \linebreak
\noindent\hyperlink{4_associative_algebras_and_their_modules}{4. Associative algebras and their modules}\dotfill \pageref*{4_associative_algebras_and_their_modules} \linebreak
\noindent\hyperlink{41_associative_algebras}{4.1 Associative algebras}\dotfill \pageref*{41_associative_algebras} \linebreak
\noindent\hyperlink{411_the_operad_}{4.1.1 The $\infty$-Operad $\mathcal{Ass}^\otimes$}\dotfill \pageref*{411_the_operad_} \linebreak
\noindent\hyperlink{412_simplicial_models_for_associative_algebras}{4.1.2 Simplicial models for associative algebras}\dotfill \pageref*{412_simplicial_models_for_associative_algebras} \linebreak
\noindent\hyperlink{413_monoidal_model_categories}{4.1.3 Monoidal Model Categories}\dotfill \pageref*{413_monoidal_model_categories} \linebreak
\noindent\hyperlink{414_rectification_of_associative_algebras}{4.1.4 Rectification of Associative Algebras}\dotfill \pageref*{414_rectification_of_associative_algebras} \linebreak
\noindent\hyperlink{42_left_and_right_modules}{4.2 Left and Right Modules}\dotfill \pageref*{42_left_and_right_modules} \linebreak
\noindent\hyperlink{421_the_operad_}{4.2.1 The $\infty$-Operad $\mathcal{L M}^{\otimes}$}\dotfill \pageref*{421_the_operad_} \linebreak
\noindent\hyperlink{422_simplicial_models_for_algebras_and_modules}{4.2.2 Simplicial models for algebras and modules}\dotfill \pageref*{422_simplicial_models_for_algebras_and_modules} \linebreak
\noindent\hyperlink{423_limits_and_colimits_of_algebras}{4.2.3 Limits and colimits of algebras}\dotfill \pageref*{423_limits_and_colimits_of_algebras} \linebreak
\noindent\hyperlink{424_free_modules}{4.2.4 Free modules}\dotfill \pageref*{424_free_modules} \linebreak
\noindent\hyperlink{425_duality_in_monoidal_categories}{4.2.5 Duality in monoidal $\infty$-categories}\dotfill \pageref*{425_duality_in_monoidal_categories} \linebreak
\noindent\hyperlink{43_bimodules}{4.3 Bimodules}\dotfill \pageref*{43_bimodules} \linebreak
\noindent\hyperlink{431_the_operad_}{4.3.1 The $\infty$-Operad $\mathcal{BM}^{\otimes}$}\dotfill \pageref*{431_the_operad_} \linebreak
\noindent\hyperlink{432_simplicial_models_for_algebras_and_modules}{4.3.2 Simplicial models for algebras and modules}\dotfill \pageref*{432_simplicial_models_for_algebras_and_modules} \linebreak
\noindent\hyperlink{433_limits_colimits_and_free_bimodules}{4.3.3 Limits, Colimits, and Free Bimodules}\dotfill \pageref*{433_limits_colimits_and_free_bimodules} \linebreak
\noindent\hyperlink{434_multilinear_maps}{4.3.4 Multilinear maps}\dotfill \pageref*{434_multilinear_maps} \linebreak
\noindent\hyperlink{435_tensor_products_and_the_bar_construction}{4.3.5 Tensor Products and the Bar Construction}\dotfill \pageref*{435_tensor_products_and_the_bar_construction} \linebreak
\noindent\hyperlink{436_associtivity_of_the_tensor_product}{4.3.6 Associtivity of the Tensor Product}\dotfill \pageref*{436_associtivity_of_the_tensor_product} \linebreak
\noindent\hyperlink{437_duality_of_bimodules}{4.3.7 Duality of Bimodules}\dotfill \pageref*{437_duality_of_bimodules} \linebreak
\noindent\hyperlink{44_modules_over_commutative_algebras}{4.4 Modules over commutative algebras}\dotfill \pageref*{44_modules_over_commutative_algebras} \linebreak
\noindent\hyperlink{5_little_cubes_and_factorizable_sheaves}{5. Little cubes and factorizable sheaves}\dotfill \pageref*{5_little_cubes_and_factorizable_sheaves} \linebreak
\noindent\hyperlink{51_definitions_and_basic_properties}{5.1 Definitions and basic properties}\dotfill \pageref*{51_definitions_and_basic_properties} \linebreak
\noindent\hyperlink{52_little_cubes_and_manifold_topology}{5.2 Little cubes and manifold topology}\dotfill \pageref*{52_little_cubes_and_manifold_topology} \linebreak
\noindent\hyperlink{521_embeddings_of_topological_manifolds}{5.2.1 Embeddings of topological manifolds}\dotfill \pageref*{521_embeddings_of_topological_manifolds} \linebreak
\noindent\hyperlink{522_variations_on_the_little_cubes_operad}{5.2.2 Variations on the little cubes operad}\dotfill \pageref*{522_variations_on_the_little_cubes_operad} \linebreak
\noindent\hyperlink{523_nonunital_algebras}{5.2.3 Nonunital $\mathbb{E}_k$-Algebras}\dotfill \pageref*{523_nonunital_algebras} \linebreak
\noindent\hyperlink{524_little_cubes_in_a_manifold}{5.2.4 Little cubes in a manifold}\dotfill \pageref*{524_little_cubes_in_a_manifold} \linebreak
\noindent\hyperlink{53_topological_chiral_homology}{5.3 Topological chiral homology}\dotfill \pageref*{53_topological_chiral_homology} \linebreak
\noindent\hyperlink{6_algebraic_structures_on_categories}{6. Algebraic structures on $\infty$-categories}\dotfill \pageref*{6_algebraic_structures_on_categories} \linebreak
\noindent\hyperlink{61_endomorphism_objects}{6.1 Endomorphism objects}\dotfill \pageref*{61_endomorphism_objects} \linebreak
\noindent\hyperlink{62_monads_and_barrbeck_theorem}{6.2 Monads and Barr-Beck theorem}\dotfill \pageref*{62_monads_and_barrbeck_theorem} \linebreak
\noindent\hyperlink{621_split_simplicial_objects}{6.2.1 Split simplicial objects}\dotfill \pageref*{621_split_simplicial_objects} \linebreak
\noindent\hyperlink{622_the_barrbeck_theorem}{6.2.2 The Barr-Beck theorem}\dotfill \pageref*{622_the_barrbeck_theorem} \linebreak
\noindent\hyperlink{623_bicartesian_fibrations}{6.2.3 BiCartesian Fibrations}\dotfill \pageref*{623_bicartesian_fibrations} \linebreak
\noindent\hyperlink{624_descent_and_the_beckchevalley_condition}{6.2.4 Descent and the Beck-Chevalley condition}\dotfill \pageref*{624_descent_and_the_beckchevalley_condition} \linebreak
\noindent\hyperlink{7_the_calculus_of_functors}{7. The calculus of functors}\dotfill \pageref*{7_the_calculus_of_functors} \linebreak
\noindent\hyperlink{71_the_calculus_of_functors}{7.1 The calculus of functors}\dotfill \pageref*{71_the_calculus_of_functors} \linebreak
\noindent\hyperlink{711_excisive_functors}{7.1.1 $n$-Excisive Functors}\dotfill \pageref*{711_excisive_functors} \linebreak
\noindent\hyperlink{712_taylor_tower}{7.1.2 Taylor Tower}\dotfill \pageref*{712_taylor_tower} \linebreak
\noindent\hyperlink{716_norm_maps}{7.1.6 Norm maps}\dotfill \pageref*{716_norm_maps} \linebreak
\noindent\hyperlink{8_algebra_in_stable_homotopy_theory}{8. Algebra in stable homotopy theory}\dotfill \pageref*{8_algebra_in_stable_homotopy_theory} \linebreak
\noindent\hyperlink{81_structured_ring_spectra}{8.1 Structured ring spectra}\dotfill \pageref*{81_structured_ring_spectra} \linebreak
\noindent\hyperlink{811_rings_and_their_modules}{8.1.1 $\mathbb{E}_1$-rings and their modules}\dotfill \pageref*{811_rings_and_their_modules} \linebreak
\noindent\hyperlink{812_recognition_principle}{8.1.2 Recognition principle}\dotfill \pageref*{812_recognition_principle} \linebreak
\noindent\hyperlink{813_change_of_ring}{8.1.3 Change of ring}\dotfill \pageref*{813_change_of_ring} \linebreak
\noindent\hyperlink{814_algebras_over_commutative_rings}{8.1.4 Algebras over Commutative Rings}\dotfill \pageref*{814_algebras_over_commutative_rings} \linebreak
\noindent\hyperlink{82_properties_of_rings_and_modules}{8.2 Properties of rings and modules}\dotfill \pageref*{82_properties_of_rings_and_modules} \linebreak
\noindent\hyperlink{821_free_resolutions_and_spectral_sequences}{8.2.1 Free resolutions and Spectral Sequences}\dotfill \pageref*{821_free_resolutions_and_spectral_sequences} \linebreak
\noindent\hyperlink{822_flat_and_projective_modules}{8.2.2 Flat and projective modules}\dotfill \pageref*{822_flat_and_projective_modules} \linebreak
\noindent\hyperlink{823_injective_objects_of_stable_categories}{8.2.3 Injective objects of stable $\infty$-categories}\dotfill \pageref*{823_injective_objects_of_stable_categories} \linebreak
\noindent\hyperlink{824_localization_and_ore_conditions}{8.2.4 Localization and Ore conditions}\dotfill \pageref*{824_localization_and_ore_conditions} \linebreak
\noindent\hyperlink{825_finiteness_properties_of_rings_and_modules}{8.2.5 Finiteness properties of rings and modules}\dotfill \pageref*{825_finiteness_properties_of_rings_and_modules} \linebreak
\noindent\hyperlink{83_the_cotangent_complex_formalism}{8.3 The cotangent complex formalism}\dotfill \pageref*{83_the_cotangent_complex_formalism} \linebreak
\noindent\hyperlink{84_deformation_theory}{8.4 Deformation theory}\dotfill \pageref*{84_deformation_theory} \linebreak
\noindent\hyperlink{85_tale_morphisms}{8.5 \'E{}tale morphisms}\dotfill \pageref*{85_tale_morphisms} \linebreak
\noindent\hyperlink{a_constructible_sheaves_and_exit_paths}{A Constructible sheaves and exit paths}\dotfill \pageref*{a_constructible_sheaves_and_exit_paths} \linebreak
\noindent\hyperlink{b_categorical_patterns}{B Categorical patterns}\dotfill \pageref*{b_categorical_patterns} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


The following is (or will eventually be) a linked list of keywords.

\hypertarget{1_stable_categories}{}\subsection*{{1. Stable $\infty$-categories}}\label{1_stable_categories}

\hypertarget{11_foundations}{}\subsubsection*{{1.1 Foundations}}\label{11_foundations}

\hypertarget{111_stability}{}\paragraph*{{1.1.1 Stability}}\label{111_stability}

\begin{itemize}%
\item [[stable (∞,1)-category]]

\begin{itemize}%
\item [[stabilization]]

\end{itemize}


\end{itemize}
\hypertarget{112_the_homotopy_category_of_a_stable_category}{}\paragraph*{{1.1.2 The homotopy category of a stable $\infty$-category}}\label{112_the_homotopy_category_of_a_stable_category}

\begin{itemize}%
\item [[triangulated category]]

\end{itemize}
\hypertarget{113_closure_properties_of_stable_categories}{}\paragraph*{{1.1.3 Closure properties of stable $\infty$-categories}}\label{113_closure_properties_of_stable_categories}

\hypertarget{114_exact_functors}{}\paragraph*{{1.1.4 Exact functors}}\label{114_exact_functors}

\begin{itemize}%
\item [[exact (∞,1)-functor]]

\end{itemize}
\hypertarget{12_stable_categories_and_homological_algebra}{}\subsubsection*{{1.2 Stable $\infty$-categories and homological algebra}}\label{12_stable_categories_and_homological_algebra}

\begin{itemize}%
\item [[homological algebra]]

\end{itemize}
\hypertarget{121_tstructures_on_stable_categories}{}\paragraph*{{1.2.1 t-Structures on stable $\infty$-categories}}\label{121_tstructures_on_stable_categories}

\begin{itemize}%
\item [[t-structure]]


\item [[t-structure on a stable (∞,1)-category]]


\item [[heart of a stable (∞,1)-category]]



\end{itemize}
\hypertarget{122_filtered_objects_and_spectral_sequences}{}\paragraph*{{1.2.2 Filtered objects and spectral sequences}}\label{122_filtered_objects_and_spectral_sequences}

\begin{itemize}%
\item [[spectral sequence]]


\item [[spectral sequence of a filtered stable homotopy type]]

\begin{itemize}%
\item [[Adams spectral sequence]]

\end{itemize}


\end{itemize}
\hypertarget{123_the_doldkan_correspondence}{}\paragraph*{{1.2.3 The Dold-Kan correspondence}}\label{123_the_doldkan_correspondence}

\begin{itemize}%
\item [[Dold-Kan correspondence]]

\end{itemize}
\hypertarget{124_the_categorical_doldkan_correspondence}{}\paragraph*{{1.2.4 The $\infty$-categorical Dold-Kan correspondence}}\label{124_the_categorical_doldkan_correspondence}

\begin{itemize}%
\item [[infinity-Dold-Kan correspondence]]


\item [[spectral sequence of a simplicial stable homotopy type]]



\end{itemize}
\hypertarget{13_homological_algebra_and_derived_categories}{}\subsubsection*{{1.3 Homological algebra and derived categories}}\label{13_homological_algebra_and_derived_categories}

\hypertarget{131_nerves_of_differential_graded_categories}{}\paragraph*{{1.3.1 Nerves of differential graded categories}}\label{131_nerves_of_differential_graded_categories}

\begin{itemize}%
\item [[dg-nerve]]

\end{itemize}
\hypertarget{132_derived_categories}{}\paragraph*{{1.3.2 Derived $\infty$-categories}}\label{132_derived_categories}

\begin{itemize}%
\item [[derived category]]

\end{itemize}
\hypertarget{133_the_universal_property_of_}{}\paragraph*{{1.3.3 The universal property of $\mathcal{D}^-(\mathcal{A})$}}\label{133_the_universal_property_of_}

\hypertarget{134_inverting_quasiisomorphisms}{}\paragraph*{{1.3.4 Inverting Quasi-isomorphisms}}\label{134_inverting_quasiisomorphisms}

\hypertarget{135_grothendieck_abelian_categories}{}\paragraph*{{1.3.5 Grothendieck abelian categories}}\label{135_grothendieck_abelian_categories}

\begin{itemize}%
\item [[Grothendieck category]]

\end{itemize}
\hypertarget{136_complexes_of_injective_objects}{}\paragraph*{{1.3.6 Complexes of injective objects}}\label{136_complexes_of_injective_objects}

\begin{itemize}%
\item [[injective object]]


\item [[chain complex]]



\end{itemize}
\hypertarget{14_spectra_and_stabilization}{}\subsubsection*{{1.4 Spectra and stabilization}}\label{14_spectra_and_stabilization}

\hypertarget{141_the_brown_representability_theorem}{}\paragraph*{{1.4.1 The Brown representability theorem}}\label{141_the_brown_representability_theorem}

\begin{itemize}%
\item [[Brown representability theorem]]

\end{itemize}
\hypertarget{142_spectrum_objects}{}\paragraph*{{1.4.2 Spectrum objects}}\label{142_spectrum_objects}

\begin{itemize}%
\item [[excisive (∞,1)-functor]]


\item [[spectrum object]]



\end{itemize}
\hypertarget{143_the_category_of_spectra}{}\paragraph*{{1.4.3 The $\infty$-category of spectra}}\label{143_the_category_of_spectra}

\begin{itemize}%
\item [[(∞,1)-category of spectra]]

\end{itemize}
\hypertarget{144_presentable_stable_categories}{}\paragraph*{{1.4.4 Presentable stable $\infty$-categories}}\label{144_presentable_stable_categories}

\begin{itemize}%
\item [[presentable (∞,1)-category]]


\item [[stable (∞,1)-category]]



\end{itemize}
\hypertarget{2_operads}{}\subsection*{{2. $\infty$-Operads}}\label{2_operads}

\hypertarget{21_foundations}{}\subsubsection*{{2.1 Foundations}}\label{21_foundations}

\hypertarget{211_from_colored_operads_to_operads}{}\paragraph*{{2.1.1 From colored operads to $\infty$-operads}}\label{211_from_colored_operads_to_operads}

\begin{itemize}%
\item [[Segal Gamma-category]]


\item [[inert morphism]]


\item [[category of operators]]


\item [[(∞,1)-operad]]



\end{itemize}
\hypertarget{212_maps_of_operads}{}\paragraph*{{2.1.2 Maps of $\infty$-operads}}\label{212_maps_of_operads}

\begin{itemize}%
\item [[morphism of (∞,1)-operads]]


\item [[fibration of (∞,1)-operads]]



\end{itemize}
\hypertarget{213_algebra_objects}{}\paragraph*{{2.1.3 Algebra objects}}\label{213_algebra_objects}

\begin{itemize}%
\item [[algebra over an (∞,1)-operad]]


\item $\mathcal{O}$-[[monoidal (∞,1)-category]]



\end{itemize}
\hypertarget{214_preoperads}{}\paragraph*{{2.1.4 $\infty$-Preoperads}}\label{214_preoperads}

\hypertarget{22_constructions_of_operads}{}\subsubsection*{{2.2 Constructions of $\infty$-Operads}}\label{22_constructions_of_operads}

\hypertarget{23_disintegration_and_assembly}{}\subsubsection*{{2.3 Disintegration and assembly}}\label{23_disintegration_and_assembly}

\hypertarget{231_disintegration_and_assembly}{}\paragraph*{{2.3.1 Disintegration and assembly}}\label{231_disintegration_and_assembly}

\hypertarget{232_generalized_operads}{}\paragraph*{{2.3.2 Generalized $\infty$-operads}}\label{232_generalized_operads}

\begin{itemize}%
\item [[generalized (∞,1)-operad]]


\item [[family of (∞,1)-operads]]



\end{itemize}
\hypertarget{233_approximations_to_operads}{}\paragraph*{{2.3.3 Approximations to $\infty$-operads}}\label{233_approximations_to_operads}

\hypertarget{234_disintegration_of_operads}{}\paragraph*{{2.3.4 Disintegration of $\infty$-operads}}\label{234_disintegration_of_operads}

\hypertarget{24_products_and_coproducts}{}\subsubsection*{{2.4 Products and coproducts}}\label{24_products_and_coproducts}

\hypertarget{241_cartesian_symmetric_monoidal_structure}{}\paragraph*{{2.4.1 Cartesian symmetric monoidal structure}}\label{241_cartesian_symmetric_monoidal_structure}

\begin{itemize}%
\item [[cartesian monoidal (∞,1)-category]]

\end{itemize}
\hypertarget{242_monoid_objects}{}\paragraph*{{2.4.2 Monoid objects}}\label{242_monoid_objects}

\begin{itemize}%
\item [[monoid]]


\item [[Gamma space]]



\end{itemize}
\hypertarget{243_cocartesian_symmetric_monoidal_structure}{}\paragraph*{{2.4.3 CoCartesian Symmetric Monoidal Structure}}\label{243_cocartesian_symmetric_monoidal_structure}

\begin{itemize}%
\item [[cocartesian monoidal (∞,1)-category]]

\end{itemize}
\hypertarget{244_wreath_products}{}\paragraph*{{2.4.4 Wreath Products}}\label{244_wreath_products}

\hypertarget{3_algebras_and_modules_over_operads}{}\subsection*{{3. Algebras and modules over $\infty$-operads}}\label{3_algebras_and_modules_over_operads}

\hypertarget{31_free_algebras}{}\subsubsection*{{3.1 Free algebras}}\label{31_free_algebras}

\hypertarget{32_limits_and_colimits_of_algebras}{}\subsubsection*{{3.2 Limits and colimits of algebras}}\label{32_limits_and_colimits_of_algebras}

\hypertarget{33_modules_over_operads}{}\subsubsection*{{3.3 Modules over $\infty$-operads}}\label{33_modules_over_operads}

\begin{itemize}%
\item [[module over an algebra over an (∞,1)-operad]]

\end{itemize}
\hypertarget{331_coherent_operads}{}\paragraph*{{3.3.1 Coherent $\infty$-operads}}\label{331_coherent_operads}

\begin{itemize}%
\item [[coherent (∞,1)-operad]]

\end{itemize}
\hypertarget{34_general_features_of_module_categories}{}\subsubsection*{{3.4 General features of module $\infty$-categories}}\label{34_general_features_of_module_categories}

\hypertarget{4_associative_algebras_and_their_modules}{}\subsection*{{4. Associative algebras and their modules}}\label{4_associative_algebras_and_their_modules}

\hypertarget{41_associative_algebras}{}\subsubsection*{{4.1 Associative algebras}}\label{41_associative_algebras}

\hypertarget{411_the_operad_}{}\paragraph*{{4.1.1 The $\infty$-Operad $\mathcal{Ass}^\otimes$}}\label{411_the_operad_}

\begin{itemize}%
\item [[associative operad]]


\item [[A-∞ operad]]


\item [[planar (∞,1)-operad]]



\end{itemize}
\hypertarget{412_simplicial_models_for_associative_algebras}{}\paragraph*{{4.1.2 Simplicial models for associative algebras}}\label{412_simplicial_models_for_associative_algebras}

\begin{itemize}%
\item [[simplicial algebra]]


\item [[model structure on simplicial T-algebras]]



\end{itemize}
\hypertarget{413_monoidal_model_categories}{}\paragraph*{{4.1.3 Monoidal Model Categories}}\label{413_monoidal_model_categories}

\begin{itemize}%
\item [[monoidal model category]]

\end{itemize}
\hypertarget{414_rectification_of_associative_algebras}{}\paragraph*{{4.1.4 Rectification of Associative Algebras}}\label{414_rectification_of_associative_algebras}

\begin{itemize}%
\item [[model structure on algebras over an operad]]


\item [[homotopy T-algebras]]/[[model structure on simplicial T-algebras]]



\end{itemize}
\hypertarget{42_left_and_right_modules}{}\subsubsection*{{4.2 Left and Right Modules}}\label{42_left_and_right_modules}

\hypertarget{421_the_operad_}{}\paragraph*{{4.2.1 The $\infty$-Operad $\mathcal{L M}^{\otimes}$}}\label{421_the_operad_}

\begin{itemize}%
\item [[(∞,1)-operad for (∞,1)-modules over an A-∞ algebra]]


\item [[(∞,1)-module]]



\end{itemize}
\hypertarget{422_simplicial_models_for_algebras_and_modules}{}\paragraph*{{4.2.2 Simplicial models for algebras and modules}}\label{422_simplicial_models_for_algebras_and_modules}

\hypertarget{423_limits_and_colimits_of_algebras}{}\paragraph*{{4.2.3 Limits and colimits of algebras}}\label{423_limits_and_colimits_of_algebras}

\hypertarget{424_free_modules}{}\paragraph*{{4.2.4 Free modules}}\label{424_free_modules}

\hypertarget{425_duality_in_monoidal_categories}{}\paragraph*{{4.2.5 Duality in monoidal $\infty$-categories}}\label{425_duality_in_monoidal_categories}

\hypertarget{43_bimodules}{}\subsubsection*{{4.3 Bimodules}}\label{43_bimodules}

\hypertarget{431_the_operad_}{}\paragraph*{{4.3.1 The $\infty$-Operad $\mathcal{BM}^{\otimes}$}}\label{431_the_operad_}

\begin{itemize}%
\item [[operad for bimodules over algebras]]


\item [[∞-bimodule]]


\item [[bitensoring]]



\end{itemize}
\hypertarget{432_simplicial_models_for_algebras_and_modules}{}\paragraph*{{4.3.2 Simplicial models for algebras and modules}}\label{432_simplicial_models_for_algebras_and_modules}

\begin{itemize}%
\item [[model structure on modules over an algebra over an operad]]

\end{itemize}
\hypertarget{433_limits_colimits_and_free_bimodules}{}\paragraph*{{4.3.3 Limits, Colimits, and Free Bimodules}}\label{433_limits_colimits_and_free_bimodules}

(\ldots{})

\hypertarget{434_multilinear_maps}{}\paragraph*{{4.3.4 Multilinear maps}}\label{434_multilinear_maps}

\begin{itemize}%
\item [[multilinear map]]


\item [[bilinear map in an (∞,1)-category]]



\end{itemize}
\hypertarget{435_tensor_products_and_the_bar_construction}{}\paragraph*{{4.3.5 Tensor Products and the Bar Construction}}\label{435_tensor_products_and_the_bar_construction}

\begin{itemize}%
\item [[tensor product of ∞-modules]]


\item [[bar construction]]



\end{itemize}
\hypertarget{436_associtivity_of_the_tensor_product}{}\paragraph*{{4.3.6 Associtivity of the Tensor Product}}\label{436_associtivity_of_the_tensor_product}

\begin{itemize}%
\item [[associativity]]

\end{itemize}
\hypertarget{437_duality_of_bimodules}{}\paragraph*{{4.3.7 Duality of Bimodules}}\label{437_duality_of_bimodules}

(\ldots{})

\hypertarget{44_modules_over_commutative_algebras}{}\subsubsection*{{4.4 Modules over commutative algebras}}\label{44_modules_over_commutative_algebras}

\hypertarget{5_little_cubes_and_factorizable_sheaves}{}\subsection*{{5. Little cubes and factorizable sheaves}}\label{5_little_cubes_and_factorizable_sheaves}

\begin{itemize}%
\item [[little cubes operad]]

\end{itemize}
\hypertarget{51_definitions_and_basic_properties}{}\subsubsection*{{5.1 Definitions and basic properties}}\label{51_definitions_and_basic_properties}

\hypertarget{52_little_cubes_and_manifold_topology}{}\subsubsection*{{5.2 Little cubes and manifold topology}}\label{52_little_cubes_and_manifold_topology}

\hypertarget{521_embeddings_of_topological_manifolds}{}\paragraph*{{5.2.1 Embeddings of topological manifolds}}\label{521_embeddings_of_topological_manifolds}

\hypertarget{522_variations_on_the_little_cubes_operad}{}\paragraph*{{5.2.2 Variations on the little cubes operad}}\label{522_variations_on_the_little_cubes_operad}

\hypertarget{523_nonunital_algebras}{}\paragraph*{{5.2.3 Nonunital $\mathbb{E}_k$-Algebras}}\label{523_nonunital_algebras}

\begin{itemize}%
\item [[nonunital ring]]


\item [[nonunital Ek-algebra]]


\item [[unitalization]]


\item [[augmented A-∞ algebra]]



\end{itemize}
\hypertarget{524_little_cubes_in_a_manifold}{}\paragraph*{{5.2.4 Little cubes in a manifold}}\label{524_little_cubes_in_a_manifold}

\hypertarget{53_topological_chiral_homology}{}\subsubsection*{{5.3 Topological chiral homology}}\label{53_topological_chiral_homology}

\begin{itemize}%
\item [[topological chiral homology]]

\end{itemize}
\hypertarget{6_algebraic_structures_on_categories}{}\subsection*{{6. Algebraic structures on $\infty$-categories}}\label{6_algebraic_structures_on_categories}

\hypertarget{61_endomorphism_objects}{}\subsubsection*{{6.1 Endomorphism objects}}\label{61_endomorphism_objects}

\hypertarget{62_monads_and_barrbeck_theorem}{}\subsubsection*{{6.2 Monads and Barr-Beck theorem}}\label{62_monads_and_barrbeck_theorem}

\begin{itemize}%
\item [[(∞,1)-monad]]


\item [[symmetric monoidal (∞,1)-category of presentable (∞,1)-categories]]



\end{itemize}
\hypertarget{621_split_simplicial_objects}{}\paragraph*{{6.2.1 Split simplicial objects}}\label{621_split_simplicial_objects}

\hypertarget{622_the_barrbeck_theorem}{}\paragraph*{{6.2.2 The Barr-Beck theorem}}\label{622_the_barrbeck_theorem}

\begin{itemize}%
\item [[Barr-Beck theorem]]

\end{itemize}
\hypertarget{623_bicartesian_fibrations}{}\paragraph*{{6.2.3 BiCartesian Fibrations}}\label{623_bicartesian_fibrations}

\hypertarget{624_descent_and_the_beckchevalley_condition}{}\paragraph*{{6.2.4 Descent and the Beck-Chevalley condition}}\label{624_descent_and_the_beckchevalley_condition}

\begin{itemize}%
\item [[higher monadic descent]]

\end{itemize}
\hypertarget{7_the_calculus_of_functors}{}\subsection*{{7. The calculus of functors}}\label{7_the_calculus_of_functors}

\begin{itemize}%
\item [[Goodwillie calculus]]

\end{itemize}
\hypertarget{71_the_calculus_of_functors}{}\subsubsection*{{7.1 The calculus of functors}}\label{71_the_calculus_of_functors}

\hypertarget{711_excisive_functors}{}\paragraph*{{7.1.1 $n$-Excisive Functors}}\label{711_excisive_functors}

\begin{itemize}%
\item [[differentiable (∞,1)-category]]


\item [[n-excisive (∞,1)-functor]]


\item [[n-reduced (∞,1)-functor]]


\item [[n-homogeneous (∞,1)-functor]]



\end{itemize}
\hypertarget{712_taylor_tower}{}\paragraph*{{7.1.2 Taylor Tower}}\label{712_taylor_tower}

\begin{itemize}%
\item [[Goodwillie-Taylor tower]]

\end{itemize}
\hypertarget{716_norm_maps}{}\paragraph*{{7.1.6 Norm maps}}\label{716_norm_maps}

\begin{itemize}%
\item [[norm map]]


\item [[Tate construction]]



\end{itemize}
\hypertarget{8_algebra_in_stable_homotopy_theory}{}\subsection*{{8. Algebra in stable homotopy theory}}\label{8_algebra_in_stable_homotopy_theory}

\begin{itemize}%
\item [[stable homotopy category]]


\item [[stable homotopy theory]]



\end{itemize}
\hypertarget{81_structured_ring_spectra}{}\subsubsection*{{8.1 Structured ring spectra}}\label{81_structured_ring_spectra}

\hypertarget{811_rings_and_their_modules}{}\paragraph*{{8.1.1 $\mathbb{E}_1$-rings and their modules}}\label{811_rings_and_their_modules}

\begin{itemize}%
\item [[A-∞ ring]], [[ring spectrum]], [[algebra spectrum]]


\item [[∞-module]]. [[module spectrum]]



\end{itemize}
\hypertarget{812_recognition_principle}{}\paragraph*{{8.1.2 Recognition principle}}\label{812_recognition_principle}

\hypertarget{813_change_of_ring}{}\paragraph*{{8.1.3 Change of ring}}\label{813_change_of_ring}

\begin{itemize}%
\item [[connective cover]]

\end{itemize}
\hypertarget{814_algebras_over_commutative_rings}{}\paragraph*{{8.1.4 Algebras over Commutative Rings}}\label{814_algebras_over_commutative_rings}

\begin{itemize}%
\item [[A-∞ algebra]]


\item [[stable Dold-Kan correspondence]]



\end{itemize}
\hypertarget{82_properties_of_rings_and_modules}{}\subsubsection*{{8.2 Properties of rings and modules}}\label{82_properties_of_rings_and_modules}

\hypertarget{821_free_resolutions_and_spectral_sequences}{}\paragraph*{{8.2.1 Free resolutions and Spectral Sequences}}\label{821_free_resolutions_and_spectral_sequences}

\hypertarget{822_flat_and_projective_modules}{}\paragraph*{{8.2.2 Flat and projective modules}}\label{822_flat_and_projective_modules}

\hypertarget{823_injective_objects_of_stable_categories}{}\paragraph*{{8.2.3 Injective objects of stable $\infty$-categories}}\label{823_injective_objects_of_stable_categories}

\hypertarget{824_localization_and_ore_conditions}{}\paragraph*{{8.2.4 Localization and Ore conditions}}\label{824_localization_and_ore_conditions}

\hypertarget{825_finiteness_properties_of_rings_and_modules}{}\paragraph*{{8.2.5 Finiteness properties of rings and modules}}\label{825_finiteness_properties_of_rings_and_modules}

\begin{itemize}%
\item [[perfect module]]


\item [[compactly generated (∞,1)-category|compactly generated]] [[stable (∞,1)-category]]


\item [[compactly generated triangulated category]]



\end{itemize}
\hypertarget{83_the_cotangent_complex_formalism}{}\subsubsection*{{8.3 The cotangent complex formalism}}\label{83_the_cotangent_complex_formalism}

\begin{itemize}%
\item [[tangent (∞,1)-category]]

\begin{itemize}%
\item [[cotangent complex]]


\item [[tangent complex]]



\end{itemize}


\end{itemize}
\hypertarget{84_deformation_theory}{}\subsubsection*{{8.4 Deformation theory}}\label{84_deformation_theory}

\begin{itemize}%
\item [[deformation theory]]

\end{itemize}
\hypertarget{85_tale_morphisms}{}\subsubsection*{{8.5 \'E{}tale morphisms}}\label{85_tale_morphisms}

\begin{itemize}%
\item [[etale morphism]]

\end{itemize}
\hypertarget{a_constructible_sheaves_and_exit_paths}{}\subsection*{{A Constructible sheaves and exit paths}}\label{a_constructible_sheaves_and_exit_paths}

\begin{itemize}%
\item [[higher homotopy van Kampen theorem]]

\end{itemize}
\hypertarget{b_categorical_patterns}{}\subsection*{{B Categorical patterns}}\label{b_categorical_patterns}

\hypertarget{references}{}\subsection*{{References}}\label{references}

The book is based on the series of articles

\begin{itemize}%
\item [[Jacob Lurie]],

\emph{[[Stable ∞-Categories]]} (\href{http://www.arxiv.org/abs/math.CT/0608228}{arxiv})

\emph{[[Noncommutative Algebra]]} (\href{http://arxiv.org/abs/math/0702299}{arXiv})

\emph{[[Commutative Algebra]]} (\href{http://arxiv.org/abs/math/0703204}{arXiv})


\item \emph{[[Deformation Theory]]} (\href{http://arxiv.org/abs/0709.3091}{arXiv})


\item \emph{$\mathbb{E}[k]$-[[Ek-Algebras|Algebras]]} (\href{http://www.math.harvard.edu/~lurie/papers/DAG-VI.pdf}{pdf})



\end{itemize}
category: reference



\end{document}