Skeletal categories

摘要

We examine in this paper skeletons of deformed image categories and their connection with structures and projections. First we state under which conditions a subcategory Σ of the deformed image category JΔ is a skeleton. Second, we consider the particular case when all deformations reduce themselves to similarities and compare Σ to the category P of structures. Third, we establish a link between skeletons and projections. Indications are given about the topological explanation of the properties which skeletons and projections possess in common as well as about the connection existing between our formalism and current applications.