nLab epipresheaf



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 AA is called epipresheaf if for any local isomorphism f:XYf:X\to Y the map A(Y)A(X)A(Y)\to A(X) is an epimorphism


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.