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- W2144039191 abstract "In the category CompHaus of compact Hausdorff spaces and continuous maps, a map is exponentiable if, and only if, it is etale (see [1]). Briefly, to prove that etale continuous maps between compact Hausdorff spaces are exponentiable, Cagliari and Mantovani build exponentials in the quasitopos of pseudotopological spaces and show that the exponentials belong to CompHaus whenever the map is etale. Using techniques developed in the study of lax algebras (see [4, 2, 3]), this can be generalized to any category CT of Eilenberg-Moore algebras for a monad T on Set satisfying the Beck-Chevalley condition (BC). Indeed, every such category can be embedded in a quasi-topos and it can be shown that exponentials of etale algebraic homomorphisms belong to CT. In this talk I will outline this proof and discuss the role of (BC) in this context." @default.
- W2144039191 created "2016-06-24" @default.
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- W2144039191 date "2006-01-01" @default.
- W2144039191 modified "2023-09-27" @default.
- W2144039191 title "On etale algebraic homomorphisms" @default.
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