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.
Keywords: (T,V)-category, compact space, proper map, Kuratowski-Mrówka Theorem
2010 MSC: 18D20, 54B30, 54D30, 54C10
Theory and Applications of Categories, Vol. 27, 2013, No. 14, pp 327-346.