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 is called epipresheaf if for any local isomorphism the map is an epimorphism
The notion is introduced in
Revised on March 6, 2013 19:44:43
by Zoran Škoda