Barbara Giunti: Projective and cofibrant constructions for tame functors

Abstract

 In this seminar, I will present the article “Abelian and model structures on tame functors” [https://arxiv.org/abs/2301.04079/], by Wojciech Chachólski, Claudia Landi, Francesca Tombari, and myself. The goal is to break down the key results of the paper for an audience of non-necessarily experts.

In detail, I will discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements, with some examples realizing these circumstances. Moreover, with some additional hypotheses, I will also show a structure theorem for cofibrant objects. If time permits, I will conclude with a general technique to generate indecomposable objects in the abelian category of functors indexed by finite posets.

Some familiarity with basic notions in category theory (such as category, functor, and natural transformation) is helpful, but I will not assume more technical knowledge from the audience.