A conglomerate of exponential supercategories of the category of finitely generated topological spaces
The author calls a full extension \({\mathcal B}\) of a category \({\mathcal A}\) an exponential supercategory of \({\mathcal A}\) provided that \({\mathcal B}\) has finite products and for each \({\mathcal B}\)-object \(B\) and each \({\mathcal A}\)- object \(A\) the functor \(B \times_ - : {\mathcal B} \to {\mathcal B}\) has a couniversal arrow \(B \times A^ B \to A\) for \(A\) with \(A^ B\) in \({\mathcal A}\). He considers the category \({\mathcal A}\) of finitely generated topological spaces as a full subcategory of the category \({\mathcal P} r{\mathcal T} op\) of pretopological spaces, and constructs, for each ordinal \(\alpha\), an exponential supercategory \({\mathcal B}_ \alpha\) of \({\mathcal A}\) in \({\mathcal P} r{\mathcal T}op\).
scientific article; zbMATH DE number 729149