nLab
semipresheaf

Definition

A semipresheaf on a semicategory CC is a semifunctor

F:C opSet F : C^{op} \to Set

from the opposite semicategory C opC^{op} of CC to the category Set of sets.

The category of semipresheaves on CC, usually denoted [C op,Set] semi[C^{op},Set]_{semi}, or just [C op,Set][C^{op},Set] when the context is clear has:

  • semifunctors F:C opSetF : C^{op} \to Set as objects;

  • natural transformations between such semifunctors as morphisms.

Created on March 30, 2010 20:12:05 by Harry (67.194.132.91)