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What (who) is upper semicomplete homomorphism - definition

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

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

Chern–Weil homomorphism

Chern–Weil theory; Chern-Weil; Weil homomorphism; Chern-Weil homomorphism; Chern-Weil theory

In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal bundles on a smooth manifold M in terms of connections and curvature representing classes in the de Rham cohomology rings of M. That is, the theory forms a bridge between the areas of algebraic topology and differential geometry.

https://en.wikipedia.org/wiki/Chern–Weil_homomorphism

Wikipedia

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