This chapter is about Métayer’s polygraphic homology of ω-categories. This homology theory was first defined in the following way: the polygraphic homology of an ω-category is the homology of the abelianization of any of its polygraphic replacements. Métayer then showed with Lafont that for every monoid, considered as an ω-category, its polygraphic homology coincides with its classical homology as a monoid. This result was then generalized to 1-categories by Guetta. In this chapter, it is proven that the polygraphic homology is the left derived functor of a linearization functor from the category of ω-categories to the category of chain complexes, respectively endowed with ω-equivalences and quasi-isomorphisms.