


Kaninjectivity of locales and spaces



Description: 
Two wellknown important facts are the characterization of the continuous lattices as the spaces injective with respect to embeddings in the category Top_{0} of T_{0} 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 Kaninjective. As a consequence, the category of stably locally compact locales (with convenient morphisms) is the Kaninjective hull of a finite subcategory of Loc. More generally, we characterize nflat embeddings in Loc for each cardinal n by means of Kaninjectivity of finite subcategories and, as a corollary, we obtain analogous characterizations of the nflat embeddings in Top_{0}. Furthermore, several wellknown subcategories of Loc and Top_{0} are Kaninjective hulls of finite subcategories, and Loc is the Kaninjective hull of a subcategory of spatial locales. This is joint work with Margarida Carvalho.

Date: 
20150519

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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