Geodesic
Change of base, Cauchy completeness and reversibility
Theory and applications of categories, Tome 10 (2002), pp. 187-219.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We investigate the effect on Cauchy complete objects of the change of base 2-functor ${\cal V}-Cat \rightarrow {\cal W}-Cat$ induced by a two-sided enrichment ${\cal V} \rightarrow {\cal W}$. We restrict our study to the case of locally partially ordered bases. The reversibility notion introduced by Walters is extended to two-sided enrichments and Cauchy completion. We show that a reversible left adjoint two-sided enrichment $F: {\cal V} \rightarrow {\cal W}$ between locally partially ordered reversible bicategories induces an adjunction $F_{\sim} \dashv F^{\sim}: \VSkCRcCat \rightharpoonup \WSkCRcCat$ between sub-categories of skeletal and Cauchy-reversible complete enrichments. We give two applications: sheaves over locales and group actions.
Classification : 18D20, 18D99.
Keywords: Enriched categories, two-sided enrichments, change of base, reversibility, Cauchy completion, sheaves. 
@article{TAC_2002_10_a9,
     author = {Anna Labella and Vincent Schmitt},
     title = {Change of base, {Cauchy} completeness and reversibility},
     journal = {Theory and applications of categories},
     pages = {187--219},
     publisher = {mathdoc},
     volume = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2002_10_a9/}
}
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Anna Labella; Vincent Schmitt. Change of base, Cauchy completeness and reversibility. Theory and applications of categories, Tome 10 (2002), pp. 187-219. http://geodesic.mathdoc.fr/item/TAC_2002_10_a9/