Category of $\mathcal{M}$-relations as a quotient of the span category

Articles in Press

Document Type : Research Paper

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Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran

10.48308/cgasa.2024.237620.1526

Abstract

We introduce $\mathcal{M}$-spans for a class $\mathcal{M}$ of morphisms in a category $\mathcal{C}$. Using the equivalence class of $\mathcal{M}$-spans under a given equivalence relation, we give the notion of an $\mathcal{M}$-relation in $\mathcal{C}$. We first show under what conditions, $\mathcal{C}$-objects together with $\mathcal{M}$-relations form a category, called the category of $\mathcal{M}$-relations and we construct a quotient of the span category as a byproduct. Then we investigate the connection between $\mathcal{M}$-relation categories and quotient span categories. We establish when a category of $\mathcal{M}$-relations is isomorphic to a quotient span category. Finally several illustrative examples are given.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 09 December 2024

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