nLab
cartesian closed model category

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Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (∞,1)-categories

Model structures

for ∞-groupoids

for ∞-groupoids

for n-groupoids

for ∞-groups

for ∞-algebras

general

specific

for stable/spectrum objects

for (∞,1)-categories

for stable (∞,1)-categories

for (∞,1)-operads

for (n,r)-categories

for (∞,1)-sheaves / ∞-stacks

Contents

Idea

A cartesian closed model category is a cartesian closed category that is equipped with the structure of a monoidal model category in a compatible way.

Revised on December 16, 2011 01:13:51 by Urs Schreiber (82.169.65.155)
Edit | Back in time (1 revision) | See changes | History | Views: Print | TeX | Source | Linked from: canonical model structure, hypercover, model category, category with weak equivalences, homotopy category, derived functor, cartesian closed category, locally cartesian closed category, model structure on simplicial sets, category of fibrant objects, model structure on topological spaces, monoidal model category, path space object, pushout-product axiom, BrownAHT, small object argument, homotopy limit, model structure on simplicial presheaves, homotopy pullback, Thomason model structure, Reedy category, generalized Reedy category, simplicial model category, enriched model category, model structure on strict omega-groupoids, spectral sequence, proper model category, Quillen equivalence, global model structure on simplicial presheaves, Quillen adjunction, model structure on sSet-enriched presheaves, model structure on chain complexes, combinatorial model category, cofibrantly generated model category, homotopy image, Reedy model structure, enriched Reedy category, model structure on functors, Kan fibrant replacement, (infinity,1)-categorical hom-space, model structure for Cartesian fibrations, model structure on dg-algebras, Quillen bifunctor, model category theory - contents, model structure on dendroidal sets, tractable model category, model structure on homotopical presheaves, model structure on an over category, Bousfield localization of model categories, model structure on dg-coalgebras, canonical model structure on Cat, model structure for complete Segal spaces, model structure for quasi-categories, model structure on algebraic fibrant objects, model structure on sSet-categories, stable model category, model structure for left fibrations, model structure on operads, transferred model structure, homotopy Kan extension, Cisinski model structure, monoid axiom in a monoidal model category, resolution, factorization lemma, simplicial Quillen adjunction, model structure on monoids in a monoidal model category, trivial model structure, model structure on simplicial algebras, cartesian closed (infinity,1)-category, model structure on reduced simplicial sets, model structure on dg-Lie algebras, cell complex, model structure on simplicial groupoids, model structure on operator algebras, model structure on algebras over an operad, model structure on spectra, model structure on modules over an algebra over an operad, Boardman-Vogt resolution, hyper-derived functor, model structure on strict omega-categories, model structure on dg-algebras over an operad, model structure on dg-categories, canonical model structure on groupoids, model structure on dg-modules, E-infinity operad, model structure for L-infinity algebras, model structure on presheaves over a test category, model structure on cosimplicial simplicial sets, compactly generated model category, contents of contents, locally presentable categories - introduction, model structure on sSet-operads, model structure for Segal operads, generalized Reedy model structure, locally cartesian closed functor, model structure for Segal categories, model structure on simplicial Lie algebras, excellent model category, algebraic model category, 2-trivial model structure, cartesian closed functor, locally cartesian closed (infinity,1)-category, locally cartesian closed model category, model structure on presheaves of spectra, fibrant object, model structure on cellular sets, model structure for dendroidal left fibrations, model structure for dendroidal Cartesian fibrations, elegant Reedy category, model structure for dendroidal complete Segal spaces, canonical model structure on Operad, projectively cofibrant diagram, model structure for infinity-groupoids, fibrant replacement, model structure on enriched categories, model topos, localization of model categories, model structure for homotopy n-types, relative category, model structure on semi-simplicial sets