Bogolyubov Institute for Theoretical Physics,
14b Metrologochna Str., 03143 Kyiv, UKRAINE
E-mail: mmtpitp@gluk.org

Categories beyond globes and cubes

We study the functorial dependence of the special category theory upon the shapes of cells to be composed. In particular, we consider the categories, whose dimensions form ordered set. Examples and applications of categories of different shapes are discussed:
    a) cyclic orders, adjunctions and closed structures;
    b) cubes and A-categories;
    c) Markl's special PROPs as a new categorical shape.