Algebra Seminar talk
2019-05-17
Josef Šlapal (Vysoké učení technické v Brně)
Closure, interior, neighbourhood and convergence in a category
Abstract:
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.