Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/89486
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. | URI: | https://hdl.handle.net/10316/89486 | DOI: | 10.1016/j.topol.2010.12.016 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Order_pres_refls_and_inj.pdf | 355.35 kB | Adobe PDF | View/Open |
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