On the notion of pseudocategory internal to a category with a 2-cell structure
Abstract
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of 2-cells arising form internal transformations in internal categories, conjugations in groups, derivations in crossed-modules or homotopies in abelian chain complexes are studied in this context, namely their behaviour as abstract 2-cells in a 2-cell structure. Issues such as naturality of a 2-cell structure are investigated. This article is intended as a preliminary starting work towards the study of the geometrical aspects of the 2-cell structures from an algebraic point of view.
Cite
@article{arxiv.0902.3626,
title = {On the notion of pseudocategory internal to a category with a 2-cell structure},
author = {N. Martins-Ferreira},
journal= {arXiv preprint arXiv:0902.3626},
year = {2014}
}
Comments
31 pages; major re-structuring with examples added;