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Bangor University - School of Computer Science

Mathematics Preprints 2007

Computational Discrete Algebra


07.10 (revised as 08.05) : ALP, M. & WENSLEY, C.D.

Automorphisms and homotopies of groupoids and crossed modules.

Summary:

This paper is concerned with the algebraic structure of groupoids and crossed modules of groupoids.
We describe the group structure of the automorphism group of a finite groupoid as a quotient of a semidirect product.
We then show that the automorphism group of a crossed module of groupoids C, in the case when the range groupoid is connected, may be determined from that of the crossed module of groups C_u formed by restricting to a single object u.
We pay particular attention to the conjugation automorphisms \wedge c_{p,q} of C.
Finally, we investigate the homotopies of a crossed module of groupoids over a single object.

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