R.F.C. Walters, Sheaves and Cauchy-complete categories, 3e Colloque sur les categories, Amiens, juillet 80, Cah. Topo. Geom. Di ., vol XXII-3, 81 36  Home/Search Document Not in Database Summary Related Articles Check |
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Change of base, Cauchy-completness and reversibility - Anna Labella Vincent (2000) (Correct)
....two sided enrichments, change of base, reversibility, Cauchy completion, sheaves. 1 Introduction Our motivation for the study of the change of base for enrichments over bicategories originated with the characterisation of sheaves as skeletal and Cauchycomplete enrichments over bicategories [Wal81], together with the fact a continuous map f : X Y yields an adjunction between the categories of sheaves f a f : Sh(Y ) Sh(X) The problem was rst to de ne a good notion of base morphism F : V W. We had in mind that such a morphism should rst induce a 2 adjunction at the level of ....
....V categories are Morita reversible equivalent then they are Morita equivalent. 21 4.2 Examples Further on we give two examples of reversible enrichments on locally posetal bicategories. Note that for the second example, the reversibility isomorphisms are not identities. Example 4. 15 (Sheaves) [Wal81] To any locale L corresponds a locally posetal 2 category C L given by: objects are the u 2 L; arrows from u to v are the w 2 L with w u v; the partial order on C L (u; v) is that of L; the composition of arrows is the intersection; the unit in u is u. Such a C L is locally ....
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R.F.C. Walters, Sheaves and Cauchy-complete categories, 3e Colloque sur les categories, Amiens, juillet 80, Cah. Topo. Geom. Di ., vol XXII-3, 81 36
Applying Enriched Categories to Quasi-Uniform Spaces. - Schmitt (2000) (Correct)
....are extended to quasi uniform spaces. Representations in terms of enrichments are given for quasi uniformly continuous maps 1 and quasi uniform space completion. The notions of enrichments and Cauchy completion are general enough and have been applied succesfully in various areas. Let us cite [Wal81] for sheaves, Be Ca St Wa83] for brations, Rut96] for ultra metric spaces, Amb Ver96] for ring representation. many others exist. Nevertheless it seems that the theory should be further developed. The original example of metric spaces is relevant. 1) The enriched functors in [Law73] are ....
R.F.C. Walters, Sheaves and Cauchy-complete categories, 3e Colloque sur les categories, Amiens, juillet 80, Cah. Topo. Geom. Di ., vol XXII-3, 81 24
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