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
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
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].