Theorems · Definition · algebraic topology

SSet.anodyneExtensions

CategoryTheory.MorphismProperty SSet

In the category of simplicial sets, an anodyne extension is a morphism that has the left lifting property with respect to fibrations, where a fibration is a morphism that has the right lifting property with respect to horn inclusions. We do not introduce a typeclass for anodyne extensions because when the Quillen model structure is fully upstreamed (TODO @joelriou), the assumption anodyneExtensions f can be spelled as [Cofibration f] [WeakEquivalence f].

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Basic

Cited by

16 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound