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Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2

By François Métayer

Also appears in collection : Categories in homotopy theory and rewriting / Catégories pour la théorie de l'homotopie et la réécriture

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.

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Citation data

  • DOI 10.24350/CIRM.V.19223903
  • Cite this video Métayer, François (26/09/2017). Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19223903
  • URL https://dx.doi.org/10.24350/CIRM.V.19223903

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