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Title: Order-preserving reflectors and injectivity
Authors: Carvalho, Margarida
Sousa, Lurdes 
Keywords: T_0-topological space; Frame; Poset enriched category; Injectivity; Kan extension; Reflective subcategory
Issue Date: 1-Nov-2011
Publisher: Elsevier
Project: PEst-C/MAT/UI0324/2011 
Serial title, monograph or event: Topology and its Applications
Volume: 158
Issue: 17
Abstract: We investigate a Galois connection in poset enriched categories between subcategories and classes of morphisms, given by means of the concept of right-Kan injectivity, and, specially, we study its relationship with a certain kind of subcategories, the KZ-reflective subcategories. A number of well-known properties concerning orthogonality and full reflectivity can be seen as a particular case of the ones of right-Kan injectivity and KZ-reflectivity. On the other hand, many examples of injectivity in poset enriched categories encountered in the literature are closely related to the above connection. We give several examples and show that some known subcategories of the category of T_0-topological spaces are right-Kan injective hulls of a finite subcategory.
DOI: 10.1016/j.topol.2010.12.016
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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