The Gpd package provides functions for computation with finite groupoids and their morphisms. The first part is concerned with the standard constructions for connected groupoids, and for groupoids with more than one component. Groupoid morphisms are also implemented, and recent work includes the implementation of automorphisms of a finite, connected groupoid: by permutation of the objects; by automorphism of the root group; and by choice of rays to each object. The automorphism group of such a groupoid is also computed, together with an isomorphism of a quotient of permutation groups. The second part implements graphs of groups and graphs of groupoids. A graph of groups is a directed graph with a group at each vertex and with isomorphisms between subgroups on each arc. This construction enables normal form computations for free products with amalgamation, and for HNN extensions, when the vertex groups come with their own rewriting systems.
Keywords for this software
References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Alp, Murat; Wensley, Christopher D.: Automorphisms and homotopies of groupoids and crossed modules (2010)
- Brown, Ronald: Crossed complexes and higher homotopy groupoids as noncommutative tools for higher dimensional local-to-global problems (2009)
- Brown, R.; Sivera, R.: Normalisation for the fundamental crossed complex of a simplicial set (2007)
- Dombi, E. R.; Gilbert, N. D.; Ruškuc, N.: Finite presentability of HNN extensions of inverse semigroups. (2005)
- Brown, Ronald: Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems (2004)
- Gilbert, N. D.: HNN extensions of inverse semigroups and groupoids. (2004)
- Brown, Ronald; Wensley, Christopher D.: Computation and homotopical applications of induced crossed modules (2003)
- Brown, R.; Moore, E. J.; Porter, T.; Wensley, C. D.: Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups (2002)