nLab
epipresheaf

Contents

Idea

The notion of epipresheaf is formally dual to the more standard notion of separated presheaf: where the latter has a monomorphism, the former has an epimorphism.

From this perspective a sheaf is a presheaf satisfying two properties: the epipresheaf condition and the “monopresheaf” (or separated presheaf) condition. Thus there are epipresheaves, monopresheaves and sheaves.

Definition

A presheaf A is called epipresheaf if for any local isomorphism f:XY the map A(Y)A(X) is an epimorphism

References

The notion is introduced in

category: sheaf theory

Revised on March 6, 2013 19:44:43 by Zoran Škoda (161.53.130.104)