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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...

morphism f from a free monoid B∗ to a free monoid A∗ is simplifiable if there is an alphabet C of cardinality less than that of B such the morphism f...

X ⊔ X → X. Given two monoids (M, μ, η) and (M′, μ′, η′) in a monoidal category C, a morphism f : M → M′ is a morphism of monoids when f ∘ μ = μ′ ∘ (f...

quotient is a monoid morphism, and induces a quotient monoid M ( S ) = M   /   ≡ S {\displaystyle M(S)=M\ /\ {\equiv _{S}}} . This monoid M ( S ) {\displaystyle...

other of morphisms. There are two objects that are associated to every morphism, the source and the target. A morphism f from X to Y is a morphism with source...

transformations of S giving rise to a monoid morphism from A∗ to the full transformation monoid TS. The image of this morphism is the transformation semigroup...

In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For...

there is a surjective semigroup morphism from S to T. For example, (Z/2Z, +) is a quotient of (Z/4Z, +), using the morphism consisting of taking the remainder...

%5B%5BWikipedia%3ARedirects+for+discussion%5D%5D+debate+closed+as+delete #REDIRECT Free monoid#Morphisms...

category, and the morphisms, which relate two objects called the source and the target of the morphism. Metaphorically, a morphism is an arrow that maps...

_{0}^{\infty }I^{n}/I^{n+1}} . A morphism f : N → M {\displaystyle f:N\to M} of graded modules, called a graded morphism or graded homomorphism , is a homomorphism...

fixed set.) The morphisms from x to x are precisely the elements of the monoid, the identity morphism of x is the identity of the monoid, and the categorical...

A dependency morphism (with respect to a dependency D) is a morphism ψ : Σ ∗ → M {\displaystyle \psi :\Sigma ^{*}\to M} to some monoid M, such that the...

have zero morphisms. In that case, if f : X → Y is an arbitrary morphism in C, then a kernel of f is an equaliser of f and the zero morphism from X to...

precisely a monoid homomorphism. Diffeomorphism Homomorphic encryption Homomorphic secret sharing – a simplistic decentralized voting protocol Morphism Quasimorphism...

theory, an epimorphism is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g1, g2: Y → Z, g 1 ∘ f =...

M and N be monoids, and let p and q be elements of the monoid M. Let φ be a morphism of monoids from M to N. It is said that the morphism φ separates...

property of universal morphisms, given any morphism h : X 1 → X 2 {\displaystyle h:X_{1}\to X_{2}} there exists a unique morphism g : A 1 → A 2 {\displaystyle...

and x•z ≤ y•z for all x, y, z in S. An ordered monoid and an ordered group are, respectively, a monoid or a group that are endowed with a partial order...

G-maps. The composition of two morphisms is again a morphism. If a morphism f is bijective, then its inverse is also a morphism. In this case f is called an...