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.