In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...
5 KB (511 words) - 14:20, 31 January 2024
itself form a monoid with respect to function composition. More generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely...
35 KB (4,447 words) - 08:24, 16 July 2024
Any monoid can be understood as a special sort of category (with a single object whose self-morphisms are represented by the elements of the monoid), and...
21 KB (2,521 words) - 21:37, 12 August 2024
classical and quantum information theory. In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action...
17 KB (2,389 words) - 13:47, 27 June 2024
terms, a monad is a monoid in the category of endofunctors of some fixed category (an endofunctor is a functor mapping a category to itself). According...
30 KB (4,467 words) - 15:23, 8 August 2024
respective categories of monoids and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup)...
22 KB (2,985 words) - 23:05, 23 February 2024
category-theoretic concept of kernel pair. In particular, kernel pairs can be used to interpret kernels in monoid theory or ring theory in category-theoretic...
7 KB (950 words) - 06:26, 1 October 2023
variant of the notion of the center of a monoid, group, or ring to a category. The center of a monoidal category C = ( C , ⊗ , I ) {\displaystyle {\mathcal...
7 KB (1,137 words) - 21:01, 23 February 2023
In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...
13 KB (1,941 words) - 22:41, 24 August 2024
In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...
14 KB (2,379 words) - 20:32, 3 February 2024