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Kan-injectivity in Top0 and Kan-projectivity in Frm
Description:  In the context of categories enriched in the category of partial order sets, we will work with KZ-reflectivity and Kan-injectivity, notions which, as we shall see, are closely related.

We will show that there is an infinite chain of small subcategories of the category Top0, whose Kan-injective hulls are KZ-reflective subcategories of Top0. Moreover, the union of this collection of KZ-reflective subcategories is the full and KZ-reflective subcategory of Top0 which objects are the sober spaces, Sob.

By duality, we define the concepts of Kan-projectivity and co-KZ-reflectivity that we study in the category Frm. Here we show that the Kan-projective hulls of the images of the subcategories of An through the contra-variant functor \mathcal{O}:Top0--->Frm, applying each topological space in the frame of the opens, are a chain of KZ-co-reflective subcategories of Frm. But their union is not contained in the subcategory of spatial lattices.

Date:  2014-07-10
Start Time:   14:30
Speaker:  Margarida Carvalho (ISCAC)
Institution:  ISCAC, Instituto Politécnico de Coimbra
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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© 2012 Centre for Mathematics, University of Coimbra, funded by

Science and Technology Foundation

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