In category theory, a regular category is a category with finite limits and coequalizers of a pair of morphisms called kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence of images, without requiring additivity. At the same time, regular categories provide a foundation for the study of a fragment of first-order logic, known as regular logic.
Read more about Regular Category: Definition, Examples, Epi-mono Factorization, Exact Sequences and Regular Functors, Regular Logic and Regular Categories, Exact (effective) Categories, See Also
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