We give several new ways of constructing spectral spaces starting with objects in abelian categories satisfying certain conditions which apply, in particular, to Grothendieck categories. For this, we consider the spaces of invariants of closure operators acting on subobjects of a given object. The key to our results is a newly discovered criterion of Finocchiaro that uses ultrafilters to identify spectral spaces along with subbases of quasi-compact open sets.
Keywords: Spectral spaces, closure operators, abelian categories
2010 MSC: 13B22, 14A05, 18E15, 54D80
Theory and Applications of Categories, Vol. 32, 2017, No. 20, pp 719-735.