nLab full sub-2-category

Context

2-Category theory

2-category theory

Contents

Definition

A 2-functor $F : C \to D$ exhibits the 2-category $C$ as a full sub-2-category of $D$ if for all objects $c_1,c_2 \in C$ the component functor $F_{c_1, c_2}$ is an equivalence of categories

$F_{c_1, c_2} : C(c_1,c_2) \stackrel{\simeq}{\to} D(F(c_1), F(c_2)) \,,$

hence if $F$ is a 2-fully-faithful 2-functor.

Properties

If $C$ and $D$ are ordinaray categories regarded as 2-categories, a full sub 2-category $F : C \hookrightarrow D$ is equivalently a full subcategory of $D$.

If $D$ is a (2,1)-category a full sub-2-category is equivalently a full sub-(∞,1)-category.

Revised on August 31, 2012 18:20:13 by Djalal? (130.238.58.207)