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.

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

The notion is introduced in

- Maxim Kontsevich, Alexander Rosenberg,
*Noncommutative spaces*, preprint MPI-2004-35 (ps, dvi)

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.