nLab epipresheaf

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

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

  , arxiv 9812158

category: sheaf theory