excellent model category
Model category theory
Producing new model structures
Presentation of -categories
for stable/spectrum objects
for stable -categories
for -sheaves / -stacks
Extra axioms on a monoidal model category that guarantee a particularly good homotopy theory of -enriched categories are referred to as excellent model category structure (Lurie).
Let 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 in an -enriched category , the localization functor is an equivalence of -enriched categories.
This is (Lurie, def. A.3.2.16).
Section A.3 in
Revised on April 5, 2015 17:31:33
by Adeel Khan