nLab
excellent model category

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Contents

Idea

Extra axioms on a monoidal model category S\mathbf{S} that guarantee a particularly good homotopy theory of S\mathbf{S}-enriched categories are referred to as excellent model category structure (Lurie).

Definition

Definition

Let S\mathbf{S} be a monoidal model category. It is called excellent if

  • it is a combinatorial model category;

  • every monomorphism if a cofibration

  • the collection of cofibrations is closed under products;

  • it satisfies the invertibility hypothesis: for any equivalence ff in an S\mathbf{S}-enriched category CC, the localization functor CC[f 1]C \to C[f^{-1}] is an equivalence of S\mathbf{S}-enriched categories.

This is (Lurie, def. A.3.2.16).

References

Section A.3 in

Revised on April 5, 2015 17:31:33 by Adeel Khan (2.243.174.221)