Categorically algebraic topology versus universal topology
This paper continues to develop the theory of categorically algebraic (catalg) topology, introduced as a common framework for the majority of the existing many-valued topological settings, to provide convenient means of interaction between different approaches. Motivated by the results of universal topology of H. Herrlich, we show that a concrete category is fibre-small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures, which is definable by topological co-axioms. (C) 2012 Elsevier B.V. All rights reserved.
categorically algebraic topology universal topology (omega-)algebra categorical topology (co)reflective subcategory functor-costructured category locale point-set lattice-theoretic topology powerset theory semi-quantale topological co-axiom topological system topological theory variety