nLab concrete (n,1)-category

Idea

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

Definition

Definition

A concrete (n,1)-category is a (n,1)-category $C$ equipped with a (n+1)-surjective functor

$$U \colon C \to nGrpd$$

to the large? (n,1)-category nGrpd of n-groupoids. We say a (n,1)-category $C$ is concretizable if and only if it admits a $(n+1)$-surjective functor $U \colon C \to Grpd$.

Related concepts

• (n,1)-category
• concrete object
• concrete category
• concrete (2,1)-category