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
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)