model category
Definitions
category with weak equivalences
weak factorization system
homotopy
small object argument
resolution
Morphisms
Quillen adjunction
Universal constructions
homotopy Kan extension
homotopy limit/homotopy colimit
Bousfield-Kan map
Refinements
monoidal model category
enriched model category
simplicial model category
cofibrantly generated model category
algebraic model category
compactly generated model category
proper model category
cartesian closed model category, locally cartesian closed model category
stable model category
Producing new model structures
on functor categories (global)
on overcategories
Bousfield localization
transferred model structure
Grothendieck construction for model categories
Presentation of -categories
(∞,1)-category
simplicial localization
(∞,1)-categorical hom-space
presentable (∞,1)-category
Model structures
Cisinski model structurefor -groupoids
for ∞-groupoids
on topological spaces
Thomason model structure
model structure on presheaves over a test category
on simplicial sets, on semi-simplicial sets
model structure on simplicial groupoids
on cubical sets
on strict ∞-groupoids, on groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
model structure on cosimplicial simplicial sets
for -groupoids
for n-groupoids/for n-types
for 1-groupoids
for -groups
model structure on simplicial groups
model structure on reduced simplicial sets
for -algebras
general
on monoids
on simplicial T-algebras, on homotopy T-algebras
on algebas over a monad
on algebras over an operad,
on modules over an algebra over an operad
specific
model structure on differential-graded commutative algebras
model structure on differential graded-commutative superalgebras
on dg-algebras over an operad
model structure on dg-modules
for stable/spectrum objects
model structure on spectra
model structure on ring spectra
model structure on presheaves of spectra
for -categories
on categories with weak equivalences
Joyal model for quasi-categories
on sSet-categories
for complete Segal spaces
for Cartesian fibrations
for stable -categories
on dg-categoriesfor -operads
on operads, for Segal operads
on algebras over an operad,
on modules over an algebra over an operad
on dendroidal sets, for dendroidal complete Segal spaces, for dendroidal Cartesian fibrations
for -categories
for (n,r)-categories as ∞-spaces
for weak ∞-categories as weak complicial sets
on cellular sets
on higher categories in general
on strict ∞-categories
for -sheaves / -stacks
on homotopical presheaves
model structure for (2,1)-sheaves/for stacks
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