nLab full sub-2-category




A 2-functor F:CDF \,\colon\, 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} \;\colon\; C(c_1,c_2) \xrightarrow{\;\; \simeq \;\;} D\big( F(c_1), F(c_2) \big) \,,

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


CC and DD can be considered as (1-)categories by forgetting their 2-morphisms, and FF can be considered as a (1-)functor via decategorification. As a result, every full sub-2-category is also a full subcategory.

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


  • Math Overflow, “When is a full sub-2-category not a full subcategory?”, web

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Last revised on December 10, 2023 at 18:38:25. See the history of this page for a list of all contributions to it.