Ryo KANDA: Every poset appears as the atom spectrum of some Grothendieck category


The atom spectrum of a Grothendieck category is a generalization of the prime spectrum of a commutative ring, and it has a natural poset structure generalizing the inclusion relation between prime ideals. In this talk, we establish a method to construct a Grothendieck category from a colored quiver, and proves that every poset appears as the atom spectrum of some Grothendieck category.