Linearization is

functorial in that the linearization of the identity map is the identity matrix, and the linearization of the composition of maps is the matrix product of the linearizations.

The aim of this short note is to indicate a

functorial construction of a locally compact group [Y.sub.A] given as

For example, the construction is not

functorial so that we cannot embed the quantum cohomology of a partial flag manifold inside the quantum cohomology of the complete flag manifold.

The former represent elements of the model whose information content cannot be stored in a computer and, therefore, must be approximated (in the preceding example the entire

functorial function).

Among the topics are a categorical perspective on connections with applications in formulating

functorial physical dynamics, something new about reconstruction, graph analysis with application to economics, a model of higher-order concurrent programs based on graph rewriting, and protecting the vertices of a graph.

The Rubato Composer music software: component-based implementation of a

functorial concept architecture.

The previous definition should make the

functorial properties of [sup.aT.sub.*] clear.

It is a sort of a dimension category, where the role of

functorial maps is played by C-space transformations which reshuffles a p-brane history for a p'-brane history or a mixture of all of them, for example.

The new concept --to be called homological or

functorial representation-- is a genuine generalization of the received notion of representation as a structure preserving map as it is used, for example, in the representational theory of measurement.

We have used [s, t] as notation for [cross product]-pairs, reserving f [cross product] g for the

functorial action of [cross product], where

Moreover, the transgression forms for this family also converge and provide a canonical and

functorial coboundary between [c.sub.m]([R.sup.v]) and Div where [R.sup.V] = [D.sup.2] is the curvature of the given connection.

First note that all steps of the construction are

functorial. Next, since g is a normal extension, we have Norm(g) = g, [bar.C] = C and [[eta].sup.norm.sub.f] = [1.sub.C].