Skip to main content Skip to section menu

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.


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.

Site footer