Algebra Seminar talk
Josef Šlapal (Vysoké učení technické v Brně)
Closure, interior, neighbourhood and convergence in a category
The natural correspondences in topology between closure, interior, neighbourhood and convergence no longer hold in an abstract categorical setting where subobject lattices are not necessarily Boolean algebras. We analyse some canonical correspondences between closure, interior, neighborhood and convergence operators in a category endowed with a subobject structure. While these correspondences coincide in general topology, the analysis highlights subtle differences which distinguish different approaches taken in the literature.