Presheaf of groups
This article defines the notion of group object in the category of set-valued presheafs|View other types of group objects
A presheaf of groups on a topological space, is a contravariant functor from the category of open sets of the topological space (under inclusion) to the category of groups.
Let be a topological space. A presheaf of groups on is the following data:
- For every open subset , a group
- For every pair of open subsets , a restriction homomorphism
- is the identity map for any
- If then
A particular case of a presheaf of groups is a sheaf of groups.