Nickolas Rollick, Department of Pure Mathematics, University of Waterloo
“Cant see the forest for the sheaves”
We devote the first half of the talk to tying up loose ends from the previous two meetings, hopefully clarifying some concepts along the way! First, we prove the claim from last meeting that a morphism of sheaves is an isomorphism if and only if all the induced morphisms on stalks are also isomorphisms. Next, we revisit the presheaf cokernel construction and show that unlike the kernel, the (presheaf) cokernel of a morphism of sheaves need not be a sheaf. This provides perfect motivation for “sheafification. Despite the wacky name, this is a really useful tool for turning a presheaf into a sheaf! If the presheaf cokernel of a morphism of sheaves is not a sheaf, we just sheafify it and carry on like nothing happened During the second half of the talk, we will introduce the universal property satisfied by sheafification and go through the explicit construction of this all-important concept.
MC 5413