Construction of Grothendieck categories with enough compressible objects using colored quivers
arXiv:1802.03546 · doi:10.1016/j.jpaa.2019.04.014
Abstract
We introduce a new method to construct a Grothendieck category from a given colored quiver. This is a variant of the construction used to prove that every partially ordered set arises as the atom spectrum of a Grothendieck category. Using the new method, we prove that for every finite partially ordered set, there exists a locally noetherian Grothendieck category such that every nonzero object contains a compressible subobject and its atom spectrum is isomorphic to the given partially ordered set.
11 pages