Modelling and Computing Homotopy Types: I

TL;DR

This paper discusses a philosophical approach to applying higher dimensional Seifert-van Kampen Theorems using groupoids, addressing foundational issues in algebraic topology and exploring applications to filtered spaces.

Contribution

It introduces a new perspective on using higher groupoids to resolve foundational anomalies in algebraic topology, bridging homology and homotopy.

Findings

Resolution of foundational anomalies in algebraic topology

Application to filtered spaces

Framework for future work on n-cubes of pointed spaces

Abstract

The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology and homotopy. We explain some applications to filtered spaces, and special cases of them, while a sequel will show the relevance to n-cubes of pointed spaces.