From Encyclopedia of Mathematics
Revision as of 17:17, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

on a topological space with values in a category (e.g. the category of sets, groups, modules, rings, etc.)

A contravariant functor from the category of open sets of and their natural inclusion mappings into . Depending on , the functor is called a pre-sheaf of sets, groups, modules, rings, etc. The morphisms corresponding to the inclusions are called restriction homomorphisms.

Every pre-sheaf generates a sheaf on (cf. Sheaf theory).


More generally, if is any small category, the term "pre-sheaf on C" is used to denote a contravariant (usually set-valued) functor defined on (cf. Site).

How to Cite This Entry:
Pre-sheaf. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.G. Sklyarenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article