Fibrewise injectivity and Kock-Zöberlein monads
نویسنده
چکیده
Using Escardó-Flagg approach to injectivity via Kock-Zöberlein monads in T0 topological spaces [3], and Hofmann’s recent study of injectivity for spaces [4], we characterize continuous maps which are injective with respect to special classes of embeddings using convergence: see [1]. In fact, convergence has been shown to be very useful in the characterization of special classes of maps, like effective descent, exponentiable and triquotient maps, but for injective continuous maps such a characterization was missing. Further, we illustrate how this approach may be a step towards a fibrewise version of Scott’s characterization of injective topological spaces as continuous lattices [5]. Finally, we investigate fibrewise injectivity in more general settings, using results of [2]. [1] F. Cagliari, M.M. Clementino, S. Mantovani, Fibrewise injectivity and Kock-Zöberlein monads, preprint. [2] M.M. Clementino, D. Hofmann, Relative injectivity as cocompleteness for a class of distributors, Theory and Applications of Categories 21 (2009), 210-230. [3] M. Escardó, R. Flagg, Semantic domains, injective spaces and monads, Electr. Notes in Theor. Comp. Science 20, electronic paper 15 (1999). [4] D. Hofmann, A four for the price of one duality principle for distributive topological spaces, preprint, arXiv:math.GN/1102.2605. [5] D. Scott, Continuous lattices, in: Springer Lecture Notes Math. 274 (1972), pp. 97-136.
منابع مشابه
Semantic domains , injective spaces and monads ( extended abstract )
Many categories of semantic domains can be considered from an order-theoretic point of view and from a topological point of view via the Scott topology. The topological point of view is particularly fruitful for considerations of computability in classical spaces such as the Euclidean real line. When one embeds topological spaces into domains, one requires that the Scott continuous maps between...
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