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.
Other articles related to "category, regular category":
... a right adjoint in A, when A is considered, using the local order structure, as a 2-category ... For a regular category C, there is an isomorphism of categories C≅Map(Rel(C)) ... For a regular category C, the allegory Rel(C) is always tabular ...
Famous quotes containing the words category and/or regular:
“I see no reason for calling my work poetry except that there is no other category in which to put it.”
—Marianne Moore (18871972)
“I couldnt afford to learn it, said the Mock Turtle with a sigh. I only took the regular course.
What was that? inquired Alice.
Reeling and Writhing, of course, to begin with, the Mock Turtle replied; and then the different branches of ArithmeticAmbition, Distraction, Uglification, and Derision.
I never heard of Uglification, Alice ventured to say.”
—Lewis Carroll [Charles Lutwidge Dodgson] (18321898)