nLab
model topos
Context
Model category theory
model category

Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$ -categories
Model structures
for $\infty$ -groupoids
for ∞-groupoids

for $n$ -groupoids
for $\infty$ -groups
for $\infty$ -algebras
general
specific
for stable/spectrum objects
for $(\infty,1)$ -categories
for stable $(\infty,1)$ -categories
for $(\infty,1)$ -operads
for $(n,r)$ -categories
for $(\infty,1)$ -sheaves / $\infty$ -stacks
$(\infty,1)$ -Topos Theory
(∞,1)-topos theory

Background
Definitions
elementary (∞,1)-topos

(∞,1)-site

reflective sub-(∞,1)-category

(∞,1)-category of (∞,1)-sheaves

(∞,1)-topos

(n,1)-topos , n-topos

(∞,1)-quasitopos

(∞,2)-topos

(∞,n)-topos

Characterization
Morphisms
Extra stuff, structure and property
hypercomplete (∞,1)-topos

over-(∞,1)-topos

n-localic (∞,1)-topos

locally n-connected (n,1)-topos

structured (∞,1)-topos

locally ∞-connected (∞,1)-topos , ∞-connected (∞,1)-topos

local (∞,1)-topos

cohesive (∞,1)-topos

Models
Constructions
structures in a cohesive (∞,1)-topos

Homotopy theory
homotopy theory , (∞,1)-category theory , homotopy type theory

flavors: stable , equivariant , rational , p-adic , proper , geometric , cohesive , directed …

models: topological , simplicial , localic , …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents
Idea
A model topos is a model category that presents an (∞,1)-topos .

This appears as Rezk, 6.1 .

Locally presentable categories: Cocomplete possibly-large categories generated under filtered colimits by small generators under small relations . Equivalently, accessible localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.

References

Created on October 15, 2012 at 17:05:45.
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