nLab
full sub-2-category

Contents

Definition

A 2-functor F:CDF : C \to D exhibits the 2-category CC as a full sub-2-category of DD if for all objects c 1,c 2Cc_1,c_2 \in C the component functor F c 1,c 2F_{c_1, c_2} is an equivalence of categories

F c 1,c 2:C(c 1,c 2)D(F(c 1),F(c 2)), F_{c_1, c_2} : C(c_1,c_2) \stackrel{\simeq}{\to} D(F(c_1), F(c_2)) \,,

hence if FF is a 2-fully-faithful 2-functor.

Properties

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

If DD 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)