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A Category of Discrete Closure Spaces Pfaltz, John L. Category closure antimatroid function Discrete systems such as sets, monoids, groups are familiar categories. The internal strucutre of the latter two is defined by an algebraic operator. In this paper we describe the internal structure of the base set by a closure operator. We illustrate the role of such closure in convex geometries and partially ordered sets and thus suggestthe wide applicability of closure systems. Next we develop the ideas of closed and complete functions over closure spaces. These can be used to establish criteria for asserting that "the closure of a functional image under $f$ is equal to the functional image of the closure". Functions with these properties can be treated as categorical morphisms. Finally, the category "CSystem" of closure systems is shown to be cartesian closed. Schloss Dagstuhl – Leibniz-Zentrum für Informatik John L. Pfaltz 2005 Is Part Of Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.04351.4 urn:nbn:de:0030-drops-1253 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.4 eng https://creativecommons.org/licenses/by/4.0/legalcode