2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133285The 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.16 pages; LaTeX2e; chapter of bookAlgebraic TopologyCategory Theory55U35 ; 18G55 ; 55P65 ; 68Q85text