# Manifold calculus adapted for simplicial complexes

## TL;DR

This paper extends manifold calculus to simplicial complexes, allowing approximation of functors from open subsets of complexes to topological spaces via a tower of polynomial functors, broadening the calculus's applicability.

## Contribution

It generalizes manifold calculus to simplicial complexes, providing an approximation framework similar to the original for manifolds.

## Key findings

- Established an analogue of the approximation theorem for simplicial complexes.
- Demonstrated that functors can be approximated by a tower of polynomial functors.
- Extended the applicability of manifold calculus to a broader class of spaces.

## Abstract

We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological spaces and prove an analogue of the approximation theorem. Namely, under certain conditions such a functor can be approximated by a tower of (appropriately adapted) polynomial functors.