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Categorical closure operators
A brief survey of the development of the theory of closure operators is presented. Results concerning the applications of the theory to epimorphisms, separation, compactness and connectedness areExpand
Closure Operators with Respect to a Functor
TLDR
A notion of closure operator with respect to a functor U is introduced. Expand
Epimorphisms in categories of separated fuzzy topological spaces
Abstract The categorical theory of closure operators is used to characterize the epimorphisms in certain categories of separated fuzzy topological spaces (in the sense of Lowen). These include the 0Expand
Closure operators, monomorphisms and epimorphisms in categories of groups
© Andrée C. Ehresmann et les auteurs, 1986, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec lesExpand
Interior operators in a category: Idempotency and heredity
Abstract Some general properties of interior operators in an arbitrary category are investigated. In particular the notions of idempotency, heredity and weak heredity are studied. Examples areExpand
Interior Operators, Open Morphisms and the Preservation Property
  • G. Castellini
  • Mathematics, Computer Science
  • Appl. Categorical Struct.
  • 1 June 2015
TLDR
The notion of open morphism with respect to an interior operator is introduced in an arbitrary category and its properties are discussed. Expand
Closure operators and connectedness
Abstract This paper introduces the notion of connectedness with respect to a closure operator on a construct X . Many classical results about topological connectednedness are extended to thisExpand
Interior Operators and Topological Connectedness
Abstract A categorical notion of interior operator is used in topology to define connectedness and disconnectedness with respect to an interior operator. A commutative diagram of Galois connectionsExpand
Closure Operators and Polarities a
ABSTRACT. Basic results are obtained concerning Galois connections between collections of closure operators (of various types) and collections consisting of subclasses of (pairs of) morphisms in 𝓂Expand
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