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Qu'est-ce (qui) est quasigroup homomorphism - définition

MORPHISM (STRUCTURE-PRESERVING MAP) BETWEEN TWO ALGEBRAIC STRUCTURES OF THE SAME TYPE

HomoMorphism; Homomorphisms; Homomorphic; E-free homomorphism; Homomorphy; Homorphic; Principal homomorphism; Surjective homomorphism; Injective homomorphism; Bijective homomorphism

Quasigroup

ALGEBRAIC STRUCTURE

Loop (algebra); Latin square property; Inverse property loop; Quasigroups; Quasi-group; Loop and quasigroup; Multiary quasigroup; Polyadic quasigroup; Multary quasigroup; Parastrophe; Divisibility (binary operation)

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative and need not have an identity element.

https://en.wikipedia.org/wiki/Quasigroup

Topological homomorphism

TVS homomorphism; Topological vector space homomorphism; TVS-homomorphism

In functional analysis, a topological homomorphism or simply homomorphism (if no confusion will arise) is the analog of homomorphisms for the category of topological vector spaces (TVSs).

https://en.wikipedia.org/wiki/Topological_homomorphism

Algebra homomorphism

RING HOMOMORPHISM PRESERVING SCALAR MULTIPLICATION

Algebra isomorphism; Homomorphism of algebras; Algebra endomorphism; Algebra automorphism

In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if and are algebras over a field (or commutative ring) , it is a function F\colon A\to B such that for all in and in ,

https://en.wikipedia.org/wiki/Algebra_homomorphism

Wikipédia

Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925).

Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra.

The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory.

A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be defined in a way that may be generalized to any class of morphisms.

https://en.wikipedia.org/wiki/Homomorphism