Cauchy completeness and causal spaces

Abstract

Following Lawvere's description of metric spaces using enriched category theory, we introduce a change in the base of enrichment that allows description of some aspects of (relativistic) causal spaces. All such spaces are Cauchy complete, in the sense of enriched category theory. Furthermore, we give sufficient conditions on a base monoidal category for which enriched categories are Cauchy complete if and only if their underlying categories are (their idempotent arrows split). Contents 7 2.4. Cauchy completeness 7 3. Cauchy completeness via idempotent splitting 8 Appendix A. Cauchy completeness 13 Appendix B. Familial epiness 13 References 17