- Seminars
- On the unicity of formal category theories
On the unicity of formal category theories
Speaker
Fosco Loregian - Max Planck Institute for Mathematics Bonn
Date
Feb 4, 2019 - Time:
16:30
Aula G
We prove an equivalence between cocomplete Yoneda structures and certain pro-arrow equipments on a 2-category K. In order to do this, we recognize the presheaf construction of a cocomplete Yoneda structure as a relative, lax idempotent monad sending each admissible 1-cell f:A→B to an adjunction P!f⊣P∗f. Each cocomplete Yoneda structure on K arises in this way from a relative lax idempotent monad "with enough adjoint 1-cells", whose domain generates the ideal of admissibles, and the Kleisli category of such a monad equips its domain with proarrows. We call these structures "yosegi". Quite often, the presheaf construction associated to a yosegi generates an ambidextrous Yoneda structure; in such a setting there exists a fully formal version of Isbell duality.
- Data pubblicazione
- Feb 1, 2019
- Contact person
- Lidia Angeleri
- Department
- Computer Science
