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.