nLab concrete (infinity,1)-category

Idea

A generalization of the notion of concrete category from category theory to (infinity,1)-category theory.

Definition

Definition

A concrete (infinity,1)-category is a (infinity,1)-category $C$ equipped with an essentially $\infty$-surjective (infinity,1)-functor

$$U \colon C \to \infty Grpd$$

to the (infinity,1)-category $\infty Grpd$ of infinity-groupoids. However every (infinity,1)-functor functor is essentially $\infty$-surjective, so the surjectivity requirement is redundant. We say an (infinity,1)-category $C$ is concretizable if and only if it admits a (infinity,1)-functor $U \colon C \to \infty Grpd$.

Related concepts

• (infinity,1)-category
• concrete object
• concrete category
• concrete (n,1)-category