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Kan-injectivity of locales and spaces
Description:  Two well-known important facts are the characterization of the continuous lattices as the spaces injective with respect to embeddings in the category Top0 of T0 topological spaces (D. Scott, 1972), and the characterization of the stably locally compact locales as the locales injective with respect to flat embeddings in the category Loc of locales (P. T. Johnstone, 1981). We show that in Loc flat embeddings are precisely those morphisms with respect to which a certain finite subcategory is Kan-injective. As a consequence, the category of stably locally compact locales (with convenient morphisms) is the Kan-injective hull of a finite subcategory of Loc. More generally, we characterize n-flat embeddings in Loc for each cardinal n by means of Kan-injectivity of finite subcategories and, as a corollary, we obtain analogous characterizations of the n-flat embeddings in Top0. Furthermore, several well-known subcategories of Loc and Top0 are Kan-injective hulls of finite subcategories, and Loc is the Kan-injective hull of a subcategory of spatial locales.
This is joint work with Margarida Carvalho.
Date:  2015-05-19
Start Time:   14:30
Speaker:  Lurdes Sousa (IP Viseu and CMUC)
Institution:  IP Viseu and CMUC
Place:  Room 5.5
Research Groups: -Algebra, Logic and Topology
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