2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224605The manuscript is an overview of the motivations and foundations lying behind Voevodsky's ideas of constructing categories similar to the ordinary topological homotopy categories. The objects of these categories are strictly related to algebraic varieties and preserve some of their algebraic invariants.This is the version published by Geometry & Topology Monographs on 29 January 2007Algebraic TopologyAlgebraic Geometry14F42,18D10,14F20,18F10text