# 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 $f:X\to Y$ the map $A(Y)\to A(X)$ is an epimorphism

## References

The notion is introduced in

category: sheaf theory

Last revised on March 6, 2013 at 19:44:43. See the history of this page for a list of all contributions to it.