An abelian group object F of BG is a sheaf on Top, together with actions yG(U) x F(U) [right arrow] F(U),

functorial in U; we write [H.sup.i](G, F) (objects of Tab) for the continuous/topological group cohomology of G with coefficients in F.

Clearly, [??] is a functor from the category [??]-Filt of coherently filtered formal sheaves of modules to the category [??]-Filt of filtered formal sheaves of modules satisfying the

functorial properties, moreover for any struct coherently filtered formal sheaf morphism [??] over [??] and for Y([[Florin].sub.1] [subset] Y([[Florin].sub.2] in [beta](Y), we get commutative diagrames of strict filtered morphisms.

El nuevo concepto de representacion, que bautizaremos como representacion homologica o

functorial por motivos que se haran obvios mas adelante, es una generalizacion del concepto de representacion concebido como aplicacion (parcialmente) preservadora de estructura, tal como ha sido elucidado por diversos autores (por ejemplo, Mundy 1986, Swoyer 1989, Krantz et al.

(in functional order) and the

functorial action of &.

Their theory supplements the recent work of Asgari-Shahidi on the

functorial life from (split and quasisplit forms of) GSpin2n to GL2n.

(10) (f, [f.sup.#]) : Spec(B) [right arrow] Spec(A), yielding a

functorial bijection

Since then, Chapoton [2] has given a

functorial interpretation of this operation.

The protocol complex satisfies some useful

functorial properties, which follow immediately from the definitions.

Nourani presents readers with comprehensive guide to new techniques with

functorial models designed to address important areas of both pure mathematics and computability theory from the algebraic point of view.

This construction is

functorial in the sense that a map f: X [right arrow] Y can also be rationalized to a map [f.sub.0]: [X.sub.0] [right arrow] [Y.sub.0] commuting with rationalisations.

For M [member of] [D.sup.b.sub.hol]([D.sub.X] there is a

functorial isomorphism

We generalize this in Section 3, defining the

functorial construction of a graded coalgebra Do C from graded coalgebras C and V.