Title: Functor calculus for multi-persistent homology
Abstract: Functor calculus is a general framework for studying functors, and comes in many flavors. We construct a variant of functor calculus, called poset cocalculus, for studying functors out of posets. Our motivation is to better understand multi-persistence modules, as these modules can be viewed as functors from R^k into a category of chain complexes. We demonstrate some properties of poset cocalculus, and apply these in concrete examples with multi-persistence modules. We finish by giving examples of poset cocalculus in other contexts, such as filtrations of simplicial complexes.
