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Proper maps for lax algebras and the Kuratowski-Mrówka theorem
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 327-346
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The characterization of stably closed maps of topological spaces as the closed maps with compact fibres and the role of the Kuratowski-Mrówka' Theorem in this characterization are being explored in the general context of lax (T,V)-algebras, for a quantale V and a Set-monad T with a lax extension to V-relations. The general results are being applied in standard (topological and metric) and non-standard (labeled graphs) contexts.

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Classification : 18D20, 54B30, 54D30, 54C10
Keywords: (T, V)-category, compact space, proper map, Kuratowski-Mrówka Theorem 
@article{TAC_2012_27_a13,
     author = {Maria Manuel Clementino and Walter Tholen},
     title = {Proper maps for lax algebras and the {Kuratowski-Mr\'owka} theorem},
     journal = {Theory and applications of categories},
     pages = {327--346},
     year = {2012},
     volume = {27},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a13/}
}
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Maria Manuel Clementino; Walter Tholen. Proper maps for lax algebras and the Kuratowski-Mrówka theorem. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 327-346. http://geodesic.mathdoc.fr/item/TAC_2012_27_a13/