G. Blanc, ' Equivalence naturelle et formules logiques en th'eorie des cat'egories. Archiv math. Logik 19 (1978), 131-137.  Home/Search   Document Not in Database   Summary   Related Articles

....Theory of Groups As shown in [2] the so called double central extensions of groups can be described as the 2 dimensional coverings with respect to the standard adjunction between groups and abelian groups. Now we extend this result to higher dimensions. Using the generalized Hopf formula [1], we show that all homology groups of groups (with coefficients in Z) can be defined in terms of higher dimensional Galois groupoids. Since this definition uses only purely categorical Galois theory, similar results might be expected for the homotopy groups in Topology and Algebraic geometry. ....

....of spans of categories (which are characterized) relating the theory to [6] As a result of this there is a natural way to define functors behaviour; equilibrium : Circ Rel, which are proven to be structure preserving. This makes explicit the connection between this work and that of [3] and [1]. Though [4] and the concept of compact closed bicategory should clearly be part of an abstract treatment of feedback, there are subtleties regarding feeding back circuits which indicate that more structures are involved. This will be discussed, as well as how the concepts of input and output may ....

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G. Blanc, ' Equivalence naturelle et formules logiques en th'eorie des cat'egories. Archiv math. Logik 19 (1978), 131-137.

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