Reflective Subcategories of C

Louis Nel
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Louis Nel: Carleton University, School of Mathematics and Statistics

Chapter Chapter 9 in Continuity Theory, 2016, pp 337-349 from Springer

Abstract: 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.

Keywords: Foundational Categories; Pathological Space; Impressive Qualifications; Canonical Factorization; Epireflective Subcategory (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31159-3_9

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