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...

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...

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...

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...

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...

respective categories of monoids and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup)...

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...

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...

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...

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...