Paths and cylinders
A homotopical category is a construction used in homotopy theory, related to but more flexible than a model category.
A homotopical category is a category with weak equivalences where on top of the 2-out-of-3-property the morphisms satisfy the 2-out-of-6-property:
- If morphisms and are weak equivalences, then so are , , and .
Every homotopical category “presents” or “models” an (infinity,1)-category , a simplicially enriched category called the simplicial localization of , which is in some sense the universal solution to inverting the weak equivalence up to higher categorical morphisms.
This definition is in paragraph 33 of
Revised on January 3, 2012 05:26:48
by Mike Shulman