Abstract homotopical methods for theoretical computer science

TL;DR

This paper reviews homotopical methods applied in theoretical computer science, focusing on model categories, Whitehead theorem generalizations, and techniques for calculating homotopy limits and colimits.

Contribution

It generalizes classical homotopical theorems and presents methods for computing homotopy limits and colimits within the context of concurrency theory.

Findings

Generalization of Whitehead theorem for CW-complexes

Methods for calculating homotopy limits and colimits

Application of homotopical methods to concurrency theory

Abstract

The purpose of this paper is to collect the homotopical methods used in the development of the theory of flows initialized by author's paper ``A model category for the homotopy theory of concurrency''. It is presented generalizations of the classical Whitehead theorem inverting weak homotopy equivalences between CW-complexes using weak factorization systems. It is also presented methods of calculation of homotopy limits and homotopy colimits using Quillen adjunctions and Reedy categories.