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Daily applications of the univalence axiom: lecture 3
Multi angle
Authors : Rijke, Egbert (Author of the conference)
CIRM (Publisher )
03B15 - Higher-order logic and type-theory
05A99 - None of the above but in this section
55U40 - Topological categories, foundations of homotopy theory
Additional resources :
https://www.cirm-math.fr/RepOrga/2689/Slides/s_rijke_3.pdf
CIRM (Publisher )
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Abstract :
The goal of my lectures is to show what mathematics looks like from the univalent point of view. In the first lecture I will describe the foundational aspects of the univalent foundations, with first applications to finite sets, descent, and the construction of the projective spaces. In the second and third lectures I will describe how the univalence axiom shows up in group theory and in combinatorics.
Keywords : univalence axiom; homotopy type theory; univalent combinatorics; formalization of mathematics; projective spaces; group theory
MSC Codes : Keywords : univalence axiom; homotopy type theory; univalent combinatorics; formalization of mathematics; projective spaces; group theory
03B15 - Higher-order logic and type-theory
05A99 - None of the above but in this section
55U40 - Topological categories, foundations of homotopy theory
Additional resources :
https://www.cirm-math.fr/RepOrga/2689/Slides/s_rijke_3.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/03/2022 Conference Date : 24/02/2022 Subseries : Research School arXiv category : Category Theory ; Logic Mathematical Area(s) : Algebra ; Combinatorics ; Logic and Foundations Format : MP4 (.mp4) - HD Video Time : 01:22:58 Targeted Audience : Researchers ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-02-24_Rijke_Part3.mp4 
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Information on the Event
Event Title : Logic and higher structures / Logique et structures supérieuresEvent Organizers : Ara, Dimitri ; Coquand, Thierry ; Mimram, Samuel Dates : 21/02/2022 - 25/02/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2689.html
Citation Data
DOI : 10.24350/CIRM.V.19889503Cite this video as: Rijke, Egbert (2022). Daily applications of the univalence axiom: lecture 3. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19889503 URI : http://dx.doi.org/10.24350/CIRM.V.19889503 |
See Also
- [Multi angle] On the ∞-topos semantics of homotopy type theory 3: all ∞-toposes have strict univalent universes / Author of the conference Riehl, Emily.
- [Multi angle] On the ∞-topos semantics of homotopy type theory 2: the simplicial model of univalent foundations / Author of the conference Riehl, Emily.
- [Multi angle] On the ∞-topos semantics of homotopy type theory 1: - a categorical semantics of dependent type theory / Author of the conference Riehl, Emily.
- [Multi angle] Daily applications of the univalence axiom: lecture 2 / Author of the conference Rijke, Egbert.
- [Multi angle] Daily applications of the univalence axiom: lecture 1 / Author of the conference Rijke, Egbert.
Bibliography
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