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Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3
Multi angle
Authors : ... (Author of the conference)
... (Publisher )
18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
... (Publisher )
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Abstract :
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.
MSC Codes : 18D05 - Double categories, $2$-categories, bicategories, hypercategories
18G10 - Resolutions; derived functors
18G50 - Nonabelian homological algebra
18G55 - Homotopical algebra
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Information on the Video
Language : EnglishAvailable date : 28/09/2017 Conference Date : 28/09/2017 Subseries : Research talks arXiv category : Category Theory ; Algebraic Topology Mathematical Area(s) : Algebra ; Logic and Foundations ; Topology Format : MP4 (.mp4) - HD Video Time : 01:22:19 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-09-28_Metayer_Part3.mp4 
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Information on the Event
Event Title : Categories in homotopy theory and rewriting / Catégories pour la théorie de l'homotopie et la réécritureDates : 25/09/2017 - 29/09/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1773.html
Citation Data
DOI : 10.24350/CIRM.V.19224603Cite this video as: (2017). Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19224603 URI : http://dx.doi.org/10.24350/CIRM.V.19224603 |
See Also
- [Post-edited] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 1 / Author of the conference ....
- [Multi angle] Type theories and polynomial monads / Author of the conference ....
- [Multi angle] Shuffles of trees / Author of the conference ....
- [Multi angle] Homotopy theory of strict $\omega$-categories and its connections with homology of monoids - Lecture 2 / Author of the conference ....
Bibliography
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- Lafont, Y., Metayer, F., & Worytkiewicz, K. A folk model structure on omega-cat. Advances in Mathematics, 224(3), 1183-1231 - http://dx.doi.org/10.1016/j.aim.2010.01.007
- Metayer, F. (2008). Cofibrant objects among higher-dimensional categories. Homology, Homotopy and Applications, 10(1), 181-203 - http://dx.doi.org/10.4310/hha.2008.v10.n1.a7
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