morphism

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morphism

[′mȯr‚fiz·əm]
(mathematics)
The class of elements which together with objects form a category; in most cases, morphisms are functions which preserve some structure on a set.
References in periodicals archive ?
Although global sections of Spec do not exist, local sections certainly do, and in abundance: these are sections over subobjects of the terminal object, and correspond to consistent choices of morphisms [[Chi].sub.A] for some objects A of W.
A model of a system S is constructed as a category ??s(X) with the objects being the equivalence classes [t] for t [element of] W??x, and the morphisms the equivalence classes of the terms representing proofs in RL.
be a morphism with components of degree p, and let f : C [approaches] [P.sub.n] be entire.
First, considering the properties of complexes of modules connected by morphisms, it proves that there always exists an algebraic scheme to classify global compositions.
which exactly induces the morphism [phi] on the level of the fundamental groups.
Suppose that there exists an extremal ray R' [subset] [bar.NE](X) such that [K.sub.X] R' < 0 and the associated contraction morphism [phi] := [Cont.sub.R']: X [right arrow] Y is a fibration to a lower dimensional variety Y.
214) that the coproduct of the objects A and B of a category b is a triple (A [??] B, [alpha], [beta]), where A [??] B is an object in b and [alpha] : A [right arrow] A [??] B, [beta] :B [beta] A [??] B are morphisms of the category b such that for every object X in b and every pair of morphisms f : A [right arrow] X, g : B [right arrow] X of b there exists a unique morphism [theta] : A [??] B [right arrow] X of b such that [theta] [theta] [alpha] = f and [theta] [??] [beta] = g.
A category C is characterized by the associativity which means that for the morphisms f : a [right arrow] b.
A left (A, [alpha])-Hom-module consists of (M, [mu]) in [??]([M.sub.k]) together with a morphism [psi] : A [cross product] M [right arrow] M, [psi](a [cross product] m) = a x m such that
(ii) A set [Hom.sub.A] (P, Q) of A-linear morphisms of an A-module P to an A-module Q naturally is an A-module.
[9] introduced the category ISet (H) consisting of intuitionistic H-fuzzy sets and morphisms between them, and studied ISet(H) in the sense of topological universe.
In what follows, the symbol G stands for a finite group consisting of morphisms and antimorphisms over [??] and containing at least one antimorphism.