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Erschienen in:
2016 | OriginalPaper | Buchkapitel
9. Reflective Subcategories of C
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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.