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# XModAlg

## Crossed modules and cat1-algebras of commutative algebras

Version 1.12

14/11/2015

Zekeriya Arvasi
Email: zarvasi@ogu.edu.tr
Homepage: http://fef.ogu.edu.tr/zarvasi
Address:
Department of Mathematics and Computer Science,
Osmangazi University, Eskişehir, Turkey

Alper Odabaş
Email: aodabas@ogu.edu.tr
Homepage: http://fef.ogu.edu.tr/matbil/aodabas/
Address:
Department of Mathematics and Computer Science,
Osmangazi University, Eskişehir, Turkey

### Abstract

The XModAlg package provides functions for computation with crossed modules of commutative algebras and cat\(^{1}\)-algebras). The current version is 1.12, released 14th November 2015 for GAP 4.7.

Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at aodabas@ogu.edu.tr.

### Copyright

© 2014-2015 Zekeriya Arvasi and Alper Odabas. XModAlg is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version.

### Acknowledgements

This documentation was prepared with the GAPDoc package of Frank Lübeck and Max Neunhöffer.

Both authors are very grateful to Chris Wensley for helpful suggestions.

This work was partially supported by TÜBİTAK (The Scientific and Technical Research Council of Turkey), project number 107T542.

### Contents

1 Introduction
2 Crossed modules
2.1 Definition and Examples
2.1-1 XModAlgebra
2.1-2 Source
2.1-3 SubXModAlgebra
2.1-4 PreXModAlgebraByBoundaryAndAction
2.2 (Pre-)Crossed Module Morphisms
2.2-1 XModAlgebraMorphism
2.2-2 Kernel
2.2-3 Image
2.2-4 SourceHom
3 Cat1-algebras
3.1 Definitions and examples
3.1-1 Cat1
3.1-2 Source
3.1-3 Cat1AlgebraSelect
3.1-4 SubCat1Algebra
3.2 Cat\(^{1}-\)algebra morphisms
3.2-1 Cat1AlgebraMorphism
3.2-2 Source
3.3 Equivalent Categories
3.3-1 PreCat1ByPreXMod
References
Index
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