In category theory, a "regular category" is a type of category that satisfies certain properties related to limits and colimits, specifically those involving equalizers and coequalizers. The concept arises in the study of different kinds of categorical structures and helps bridge the gap between abstract algebra and topology. Here are key aspects of regular categories: 1. **Pullbacks and Equalizers**: Regular categories have all finite limits, which includes pullbacks and equalizers.
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A regular category has finite limits, image factorizations into regular epimorphisms followed by monomorphisms, and pullback-stable regular epimorphisms.