  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.
