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A groupoid should be thought of as a group with many objects, or with many identities. A precise definition is given below. A groupoid with one object is essentially just a group. So the notion of groupoid is an extension of that of groups. It gives an additional convenience, flexibility and range of applications, so that even for purely group-theoretical(More)
A generalised tensor product G 0 H of groups G, H has been introduced by R. Brown and J.-L. Loday in [3,4]. It arises in applications in homotopy theory of a generalised Van Kampen theorem. The reason why G 0 H does not necessarily reduce to GUh Oz Huh, the usual tensor product over Z of the abelianisations, is that it is assumed that G acts on H (on the(More)
This work is devoted to an interpretation and computation of the first homology groups of the small category given by a rewriting system. It is shown that the elements of the first homology group may be regarded as the equivalence classes of the flows in a graph of the rewriting system. This is applied to calculating the homology groups of asynchronous(More)