Marek Zawadowski
Abstract properties of many-to-one shapes

I will discuss what it should be the category of shapes of cells in a full subcategory of the category of computads/poligraphs (like one-to-one, many-to-one or all computads/poligraphs). Then, I will introduce a notion of a graded tensor theory (GT-theory) which aim at capturing the abstract properties of such categories of shapes. The category of ordered face structures and monotone maps is the category of shapes of many-to-one computads. The monotone maps of ordered face structures are the most fundamental and they generate three larger interesting classes of morphisms that I will discuss briefly at the end of the talk.