The study of the deficiency of a category arises from the problem of understanding what is a presentation of a category with the least number of equations and, therefore, avoiding redundancy.
I have been studying deficiency within the context of descent and lifting of biadjoints (within the context of categories, 2-categories, Gray-categories and tricategories). The basic general results of low dimensional categories are going to be in the first part of my PhD thesis.
In this talk, after some background, I will introduce the 1-dimensional case. I will present my very first results related to deficiency. With this motivation, I will introduce the appropriate definition of deficiency of a category.
This is part of my PhD work under supervision of Prof. Maria Manuel Clementino.