Constant morphisms and constant subcategories
Abstract:In a category supplied with a factorization system for morphisms and a fixed subcategory of constant objects, we introduce suitable notions of constant morphism and of the corresponding right and left constant subcategories.
The nature of constant morphisms we use captures two important features of constant subcategories:
left-constant subcategories are right-constant in the dual category and the subcategory of constant objects contains relevant information on these subcategories.
Furthermore, we present characterizations of constant subcategories in several contexts.
Namely, we extend the characterization of disconnectednesses obtained by Husek and Pumplun, via terminal fans, to our context.
