Topologicality, Completeness and Cocompleteness of the Category of Structural Spaces

Abstract

After introducing the notion of operant relative to a base, we present the concepts of structural space and structural morphism with respect to a given operant. We prove, under mild conditions, that the category of structural spaces and structural morphisms is a topological category. Concluding that when the underlying category is complete or cocomplete, so is the category of structural spaces, and that limits
or colimits are concrete. Several illustrative examples are furnished that show the diversity of the concept of a structural space.