Synthetic mathematics, logic-affine computation and efficient proof systems / Mathématiques synthétiques, calcul logique affine et systèmes de preuve efficients

Collection Synthetic mathematics, logic-affine computation and efficient proof systems / Mathématiques synthétiques, calcul logique affine et systèmes de preuve efficients

Organizer(s) Blechschmidt, Ingo ; Cohen, Liron ; Coquand, Thierry ; Negri, Sara ; Schuster, Peter

Date(s) 08/09/2025 - 12/09/2025

linked URL https://conferences.cirm-math.fr/3377.html

3 5

Synthetic perspectives on the Yoneda lemma

The Yoneda lemma, considered to be the fundamental theorem of category theory, is difficult to explain because its statement is both abstract and obscure. But in synthetic category theory, "functionality" and "naturality" are automatic, and the Yoneda lemma can be understood as an "arrow induction" principle that applies in covariant or contravariant settings.

Information about the video

Date of recording 09/09/2025
Date of publication 02/10/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20388203
Cite this video Riehl, Emily (09/09/2025). Synthetic perspectives on the Yoneda lemma. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20388203
URL https://dx.doi.org/10.24350/CIRM.V.20388203

Domain(s)

Category Theory

Bibliography

RIEHL, Emily et SHULMAN, Michael. A type theory for synthetic ∞-categories, Higher Structures 1 (2017), no. 1, 116–193 - https://dx.doi.org/10.21136/HS.2017.06
RIEHL, Emily. Could∞-category theory be taught to undergraduates. Notices of the American Mathematical Society, 2023, vol. 70, no 5, p. 727-736. - https://doi.org/10.1090/noti2692