Change of Base, Cauchy Completeness and Reversibility
نویسندگان
چکیده
We investigate the effect on Cauchy complete objects of the change of base 2-functor V-Cat → W-Cat induced by a two-sided enrichment V → W. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced in [Wal82] is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment F : V → W between locally partially ordered reversible bicategories induces an adjunction F∼ ⊣ F ∼ : V-SkCRcCat ⇀ W-SkCRcCat between sub-categories of skeletal and Cauchy-reversible complete enrichments. We give two applications: sheaves over locales and group actions.
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