Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Created:
Partial model categories are one of the many intermediate notions between relative categories and model categories.
They axiomatize those properties of model categories that only involve weak equivalences.
A partial model category is a relative category such that its class of weak equivalences satisfies the 2-out-of-6 property (if sr and ts are weak equivalences, then so are r, s, t, tsr) and admits a 3-arrow calculus, i.e., there are subcategories U and V (which can be thought of as analogues of acyclic cofibrations and acyclic fibrations) such that U is closed under cobase changes (which are required to exist), V is closed under base changes, and any morphism can be functorially factored as the composition vu for some u∈U and v∈V.
If (C,W) is a partial model category, then any Reedy fibrant replacement of the Rezk nerve N(C,W) is a complete Segal space.
1 to 3 of 3