nLab Author — John Baez

Overview

John Baez has contributed to 587 nLab pages.

Most recent contributions

All pages contributed to

• (-1)-category
• (-2)-category
• (infinity,1)-Grothendieck construction
• (infinity,1)-topos
• 0-category
• 2-group
• 2-Hilbert space
• 2-monad
• 2-morphism
• 2-morphisms > history
• 2-rig
• 2-vector space
• 2009 August changes
• 2009 July changes
• 2009 June changes
• 2009 September changes
• 24
• 3-group
• 3-groupoid
• Ab
• abelian category
• abelian group
• abelian variety
• About
• abstraction
• action
• action groupoid
• action of a category on a set
• Adams operation
• adhesive category
• adjoint functor
• adjoint functor theorem
• adjoint lifting theorem
• adjunction
• affinoid algebra
• Albanese variety
• algebrad
• algebraic category
• algebraic group
• algebraic space
• algebraic stack
• algebraic theory
• ambidextrous adjunction
• analytic manifold
• arithmetic pretopos
• arrow category
• Artin gluing
• Artin reciprocity law
• associator
• atomic Boolean algebra
• atomic geometric morphism
• augmented simplicial set
• automorphism
• axiom of choice
• Azumaya algebra
• bar construction
• Batanin omega-category
• bi-Heyting topos
• bialgebra
• bicategory
• bifibration
• bimonoid
• biproduct
• biring
• Bob Walters
• BoolAlg
• Boolean algebra
• Boolean ring
• Bousfield localization
• Bousfield localization of triangulated categories
• braided monoidal 2-category
• braided monoidal category
• braided monoidal natural transformation
• braiding
• Brauer group
• BV-BRST formalism
• Bénabou-Roubaud theorem
• c-theorem
• calculus of fractions
• Calculus of fractions and homotopy theory
• canonical model structure on Cat
• cardinal number
• cartesian monoidal category
• Cartesian morphism
• Cat
• categorial grammar
• categorification via groupoid schemes
• category
• category algebra
• category of fractions
• category theory
• category with duals
• category with weak equivalences
• Catégories Tannakiennes
• Cauchy complete category
• Cayley-Dickson construction
• center of an additive category
• characteristic class
• Chow motive
• class equation
• classifying topos
• classifying topos of a localic groupoid
• clique
• closed category
• closed monoidal category
• club
• coalgebra
• cocomplete category
• cocontinuous functor
• coextension of scalars
• cofibrantly generated model category
• coherence theorem for symmetric monoidal bicategories
• coherent module
• coherent ring
• coherent sheaf
• colimit
• combinatorial Hopf algebra
• combinatorial model category
• comma category
• commutative monoid
• commutative monoid in a symmetric monoidal category
• commutative monoidal category
• comonoid
• compact closed category
• compact object
• compact symplectic group
• complement
• complete category
• composition
• computad
• computational trilogy
• computer science
• conceptual completeness
• conical space
• connected limit
• connected topos
• conservative functor
• convex set
• convex space
• coproduct
• core groupoid
• core of a ring
• corepresentation
• cosmic censorship hypothesis
• cosmic cube
• cospan
• coverage
• crossed complex
• crystallographic group
• D'Auria-Fré-Regge formulation of supergravity
• D-module
• dagger category
• dagger-compact category
• database of categories
• David Corfield
• Day convolution
• de Rham space
• decalage
• definitional equality
• Deligne tensor product of abelian categories
• Deligne's theorem on tensor categories
• dense functor
• derived affine scheme
• Dieudonné determinant
• diffeological space
• dinatural transformation
• directed graph
• displayed category
• distributive category
• distributive lattice
• distributive law
• division algebra
• division algebra and supersymmetry
• Dold-Kan correspondence
• Doplicher-Roberts reconstruction theorem
• double bicategory
• double category
• double negation
• dualizable object
• E-infinity algebra
• Eckmann-Hilton argument
• effective action functional
• Eilenberg-Mac Lane space
• Eilenberg-Moore category
• Eilenberg-Watts theorem
• Eilenberg-Zilber theorem
• electromagnetic field
• elementary embedding
• endofunctor
• enriched category
• epimorphism
• equalizer
• equivalence
• equivalence in a 2-category
• equivalence of 2-categories
• essential fiber
• essentially algebraic theory
• essentially injective functor
• ETCS
• exact functor
• exponentiable functor
• extended functorial field theory
• extensive category
• exterior algebra
• faithful > history
• Fermat theory
• fiber
• fiber functor
• field
• field extension
• filtered colimit
• finite limit
• finitely generated module
• FinRel
• FinSet
• flat module
• formal category theory
• foundation of mathematics
• framed little n-disk operad
• free cocompletion
• free monad
• Frobenius algebra
• Frobenius morphism
• Frobenius reciprocity
• FRS-theorem on rational 2d CFT
• full > history
• function
• functor
• functor category
• Functorial Semantics of Algebraic Theories
• fundamental groupoid
• fundamental theorem of covering spaces
• funny tensor product
• Gabriel-Rosenberg theorem
• Gabriel–Ulmer duality
• General Discussion
• general linear group
• generalized element
• generalized smooth space
• generalized the
• generic interval
• geometric morphism
• Giry monad
• globular operad
• graded vector space
• graph
• graphic category
• Grassmann algebra > history
• Green-Schwarz mechanism
• Grothendieck group
• Grothendieck ring
• Grothendieck's Galois theory
• group
• group algebra
• group extension
• group object
• groupoid
• Grp
• GUT
• heap
• Hegelian taco
• higher category theory
• higher category theory and physics
• hom-functor
• HomePage
• homomorphism
• homotopical category
• homotopy coherent nerve
• homotopy groups of spheres
• homotopy hypothesis
• homotopy n-type
• homotopy T-algebra
• homset > history
• Hopf algebra
• Hopf algebroid
• How to get started
• HowTo
• Hoàng Xuân Sính
• hypergraph category
• hypermonoid
• hyperring
• identity > history
• incompleteness theorem
• infinity-stack
• internalization
• inverse image
• Isbell duality
• Isbell envelope
• isomorphism
• iterated monoidal category
• J-homomorphism
• Jacques Penon
• James Dolan
• Jiří Rosický
• John Baez
• Jordan algebra
• Jordan-Lie-Banach algebra
• k-surjectivity > history
• K3 surface
• Kan extension
• kappa-symmetry
• Kapranov-Voevodsky 2-vector space
• kernel pair
• Kähler differential
• L-infinity-algebra
• Lagrangian Grassmannian
• Lambda-ring
• Langlands program
• Lawvere theory
• lax functor
• lax monoidal category
• lax natural transformation
• lax-idempotent 2-monad
• Lectures on n-Categories and Cohomology
• Lex
• Lie algebra cohomology
• Lie groupoid
• Lie's three theorems
• Lie-Rinehart pair
• lifting property
• Light Mills > history
• limit
• linear functor
• linear operad
• little cubes operad
• locally finitely presentable category
• locally presentable category
• locally small category
• Lorentz group
• magma
• manifold
• Manuel Bullejos
• Marcelo Aguiar
• math blogs
• Max Kelly
• measurable cardinal
• measurable space
• measure space
• Mitchell-Bénabou language
• modal type
• model category
• model structure on chain complexes
• model structure on simplicial sets
• model structure on topological spaces
• module
• module over a quantale
• moduli space of curves
• moduli stack of elliptic curves
• monad
• monadic adjunction
• monadic descent
• monadic functor
• monadicity theorem
• monoid
• monoidal category
• monoidal functor
• monoidal natural transformation
• monomorphism
• Moore complex
• Morita equivalence
• morphism
• morphism of finite presentation
• motivic Galois group
• music theory
• n-fold category
• n-fold complete Segal space
• natural isomorphism
• natural numbers object
• natural transformation
• nCob
• nerve
• New Spaces for Mathematics and Physics
• nominal set
• normal subgroup
• normed division algebra
• NQ-supermanifold
• Nullstellensatz
• object
• octonion
• octonionic Hopf fibration
• omega-category
• Omega-group
• operad
• opetope
• oplax monoidal functor
• opposite category
• optics
• over-topos
• p-adic Hodge theory
• para construction
• partial order
• pentagon decagon hexagon identity
• perfect field
• periodic table
• permutation groupoid
• Peter May
• Picard 3-group
• pitch-class
• plethory
• plethysm
• Poincaré duality space
• Polish space
• polynomial
• Pontrjagin dual
• poset > history
• pre-abelian category
• pre-Lie algebra
• pre-net
• preorder
• preserved limit
• preset
• presheaf
• pretopological space
• pretopos
• principle of equivalence
• prismatic cohomology
• product > history
• profunctor
• projective module
• PROP
• proset > history
• pseudofunctor
• pseudomonoid
• pseudonatural transformation
• pullback
• pure motive
• Pursuing Stacks
• pushout
• quandle
• quantum information theory via dagger-compact categories
• quasi-limit
• quasigroup
• quaternionic unitary group
• Quillen equivalence
• Quillen exact category
• Quiv
• quiver
• rack
• rational function
• rational homotopy theory
• rational number
• rational topological space
• reconstruction theorem
• redirect
• Reedy category
• reflective subcategory
• reflexive graph
• regular category
• regular monomorphism
• Rel
• relevance monoidal category
• renormalization
• representable functor
• representation
• representation ring
• restriction of scalars
• ribbon category
• Riccati equation
• rig
• rig category
• rigid monoidal category
• Ring
• ring
• ring of Witt vectors
• Ross Street
• Récoltes et semailles
• Sandbox
• Schanuel topos
• Schur functor
• Schur's lemma
• semi-simplicial set
• semicartesian monoidal category
• semigroup
• semigroups > history
• SemiLat
• semilattice
• semisimple abelian category
• semisimple algebra
• semisimple category
• semisimple object
• semisimple ring
• separable algebra
• separable field extension
• separable functor
• Serre fibration
• Set
• set
• sheaf and topos theory
• Sheaves in Geometry and Logic
• shelf
• short map
• simple algebra
• simple object
• simplex category
• simplicial complex
• simplicial localization
• singular simplicial complex
• site
• skeletal > history
• SL(2,O)
• small category
• smooth groupoid
• smooth infinity-groupoid
• source
• span
• special lambda-ring
• special linear group
• special unitary group
• species
• Spin(5)
• Spin(6)
• split exact sequence
• star-autonomous category
• Steenrod homology
• Street fibration
• strict 2-category
• strict monoidal category
• string diagram
• string field theory
• String Lie 2-algebra
• strong monad
• structure type
• stuff > history
• stuff type
• stuff, structure, property
• subcategory
• super Poincaré Lie algebra
• super vector space
• suplattice
• Swapneel Mahajan
• Sweedler notation
• sylleptic 3-group
• symmetric algebra
• symmetric function
• symmetric monoidal category
• symmetric monoidal dagger-category
• symmetric monoidal functor
• symmetric operad
• symmetric space
• symplectic Lie n-algebroid
• Tall-Wraith monoid
• Tambara module
• tangle hypothesis
• Tannaka duality
• Tannaka-Krein theorem
• target
• tensor power
• tensorial strength
• thin category
• Thomason model structure
• Timeline of category theory and related mathematics
• Todd Trimble
• topos
• torsor
• toset > history
• total category
• totally ordered set > history
• Towards Higher Categories
• triangle identities
• Trimble n-category
• Trimble on ETCS I
• true proposition
• twistor space
• Tôhoku
• unitary group
• unitary morphism
• unitor
• universal enveloping E-n algebra
• universality class
• unramified morphism
• Urs Schreiber
• variety of algebras
• Vect
• vector space
• vertex operator algebra
• vertical categorification
• vertical transformation
• very commutative object
• Vietoris complex
• Wedderburn-Artin theorem
• Weil zeta function
• William Lawvere
• Young diagram
• Zariski site
• zero
• |cocomplete category > history
• étendue