Weak equivalence between simplicial sets

In mathematics, especially algebraic topology, a weak equivalence between simplicial sets is a map between simplicial sets that is invertible in some weak sense. Formally, it is a weak equivalence in some model structure on the category of simplicial sets (so the meaning depends on a choice of a model structure.)

An ∞-category can be (and is usually today) defined as a simplicial set satisfying the weak Kan condition. Thus, the notion is especially relevant to higher category theory.