Homotopy category of an ∞-category

In mathematics, especially category theory, the homotopy category of an ∞-category C is the category where the objects are those in C but the hom-set from x to y is the quotient of the set of morphisms from x to y in C by an appropriate equivalence relation. If an ∞-category is defined as a weak Kan complex (usual definition), then the construction is due to Boardman and Vogt, who also gave the definition of an ∞-category as a weak Kan complex.

Source: Wikipedia — Homotopy category of an ∞-category (CC BY-SA 4.0)