In mathematics, categories allow one to formalize notions involving abstract structure and processes which preserve structure. Categories appear in virtually every branch of modern mathematics and are a central unifying notion. The study of categories in their own right is known as category theory.
For more extensive motivational background and historical notes, see category theory and the list of category theory topics.
Category mathematics - Definition.
A category C consists of
Including:
A morphism f : a → b is called
a monomorphism (or monic) if fg1 = fg2 implies g1 = g2 for all morphisms g1, g2 : x → a.
an epimorphism (or epic) if g1f = g2f implies g1 = g2 for all morphisms g1, g2 : b → x.See also:
A category C consists of
a class ob(C) of objects:
a class hom(C) of morphisms. Each morphism f has a unique source object a and target object b where a and b are in ob(C). We write f: a → b, and we say "f is a morphism from a to b". We write hom(a, b) (or homC(a, b)) to denote the hom-class of all morphisms from a to b. (Some a ...
