A Relation Between Closure Operators on a Small Category and Its Category of Presheaves |
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Authors: | S N Hosseini S SH Mousavi |
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Institution: | (1) Mathematics Department, Shahid Bahonar University of Kerman, Kerman, Iran;(2) Mathematics Department, Vali-ASR University of Rafsandjan, Rafsandjan, Iran |
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Abstract: | In this paper we show that each factorization structure on a small category , satisfying certain conditions, yields a presheaf on and a morphism of presheaves . We then give connections, and set up one to one correspondences, between subclasses of the following classes: (a) closure operators on (b) subobjects of (c) morphisms from to (d) weak Lawvere–Tierney topologies (e) weak Grothendieck topologies (f) closure operators on . |
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Keywords: | factorization structure Grothendieck topology (idempotent modal) closure operator Lawvere– Tierney topology |
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