Definition
A category C is called regular if it satisfies the following three properties:
- C is finitely complete.
- If f:X→Y is a morphism in C, and
- is a pullback, then the coequalizer of p0,p1 exists. The pair (p0,p1) is called the kernel pair of f. Being a pullback, the kernel pair is unique up to a unique isomorphism.
- If f:X→Y is a morphism in C, and
- is a pullback, and if f is a regular epimorphism, then g is a regular epimorphism as well. A regular epimorphism is an epimorphism which appears as a coequalizer of some pair of morphisms.
Read more about this topic: Regular Category
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