FG1 Seminar talk

2011-05-13
Josef Šlapal
Categorical neighborhood operators

Abstract:
We introduce and study a concept of neighborhood operator on a category. Such an operator is obtained by assigning a suitably axiomatized stack of subobjects - the neighbourhoods - to every subobject of each object in the category. We define in a natural way and discuss closure and interior operators, convergence, separation and compactness with respect to a neighborhood operator.