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arXiv · 2109.11381

On the cocartesian image of preorders and equivalence relations in regular categories

Dominique Bourn
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Abstract

In a regular category $\mathbb E$, 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 $R[f]\vee S$ among the preorders. We investigate here some conditions ensuring the existence of these cocartesian images or equivalently of these suprema. They applied to two very dissimilar contexts: any topos $\mathbb E$ with suprema of chains of subobjects or any $n$-permutable regular category.

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Dominique Bourn. 2021-09-23. On the cocartesian image of preorders and equivalence relations in regular categories. https://arxiv.org/abs/2109.11381

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