Abstract
In a category supplied with a factorization system for morphisms and a fixed subcategory of constant objects, we introduce suitable notions ofconstant morphism and of the correspondingright andleft constant subcategories. The nature of constant morphisms we use captures two important features of constant subcategories: left-constant subcategories are right-constant in the dual category and the subcategory of constant objects contains relevant information on these subcategories. Furthermore, we present characterizations of constant subcategories in several contexts. Namely, we extend the characterization of disconnectednesses obtained by Hušek and Pumplün, via terminal fans, to our context.
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The author acknowledges financial support by Centro de Matemática da Universidade de Coimbra.
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Clementino, M.M. Constant morphisms and constant subcategories. Appl Categor Struct 3, 119–137 (1995). https://doi.org/10.1007/BF00877632
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DOI: https://doi.org/10.1007/BF00877632