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Journal Articles Applied Categorical Structures Year : 2022

On the Cocartesian Image of Preorders and Equivalence Relations in Regular Categories

Abstract

In a regular category E, the direct image along a regular epimorphism f of a preorder is not a preorder in general. In Set, its best preorder approximation is then its cocartesian image above f . In a regular category, the existence of such a cocartesian image above f of a preorder S is actually equivalent to the existence of the supremum R[ f ] ∨ S among the preorders. We investigate here some conditions ensuring the existence of these cocartesian images or equivalently of these suprema. They apply to two very dissimilar contexts: any topos E with suprema of countable chains of subobjects or any n-permutable regular category.

Dates and versions

hal-04353392 , version 1 (19-12-2023)

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Dominique Bourn. On the Cocartesian Image of Preorders and Equivalence Relations in Regular Categories. Applied Categorical Structures, 2022, 30 (6), pp.1153-1176. ⟨10.1007/s10485-022-09686-w⟩. ⟨hal-04353392⟩
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