The notion of pseudocategory 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 from 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 geometric aspects of the 2-cell structures from an algebraic point of view.
"On the notion of pseudocategory internal to a category with a 2-cell structure." Tbilisi Math. J. 8 (1) 107 - 141, June 2015. https://doi.org/10.1515/tmj-2015-0007