Reflective Subcategories of C

Abstract

Despite its impressive qualifications, the foundational category C (or one of its rigid-reflective alternatives C _r and C _p ) cannot by itself be the ultimate laboratory for continuity theory. Being a foundational category, it is inevitably infested with pathological spaces. We want to get rid of them while retaining the desirable properties of the category as a whole. By forming a reflective subcategory we automatically retain dicompleteness, thus also canonical factorizations. By forming an enriched reflective subcategory we retain poweredness along with dicompleteness.