A category in category theory is a collection of objects and morphisms between them. In programming, typically types
act as the objects and functions as morphisms.
To be a valid category 3 rules must be met:
There must be an identity morphism that maps an object to itself.
Where a is an object in some category,
there must be a function from a -> a.
Morphisms must compose.
Where a, b, and c are objects in some category,
and f is a morphism from a -> b, and g is a morphism from b -> c;
g(f(x)) must be equivalent to (g • f)(x).
Composition must be associative
f • (g • h) is the same as (f • g) • h
Since these rules govern composition at very abstract level, category theory is great at uncovering new ways of composing things.
Category
A category in category theory is a collection of objects and morphisms between them. In programming, typically types act as the objects and functions as morphisms.
To be a valid category 3 rules must be met:
ais an object in some category, there must be a function froma -> a.a,b, andcare objects in some category, andfis a morphism froma -> b, andgis a morphism fromb -> c;g(f(x))must be equivalent to(g • f)(x).f • (g • h)is the same as(f • g) • hSince these rules govern composition at very abstract level, category theory is great at uncovering new ways of composing things.
Ссылки