nLab
homotopy 2-category

Idea

The homotopy 2-category of an (∞,n)-category $𝒞$ is the 2-category ${\mathrm{Ho}}_2(𝒞)$ with the same objects and 1-morphisms as $𝒞$ and with the 2-morphisms being the equivalence classes of 2-morphisms of $𝒞$.

In other words, for every pair $X,Y$ of objects in $𝒞$, the hom-category ${\mathrm{Ho}}_2(𝒞)(X,Y)$ is the ordinary homotopy category of the $(\mathrm{\infty },n-1)$-category $𝒞(X,Y)$.

Related concepts

• homotopy category