Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2
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In the first part, we describe the canonical model structure on the category of strict $\omega$-categories and how it transfers to related subcategories. We then characterize the cofibrant objects as $\omega$-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular $\omega$-category, this polygraphic point of view will lead us to an alternative definition of monoid homology, which happens to coincide with the usual one.