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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.
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