The Hopf category of Frobenius algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909251417407488 |
|---|---|
| author | Großkopf, Paul Vercruysse, Joost |
| author_facet | Großkopf, Paul Vercruysse, Joost |
| contents | We show that the universal measuring coalgebras between Frobenius algebras turn the category of Frobenius algebras into a Hopf category (in the sense of Batista-Caenepeel-Vercruysse), and the universal comeasuring algebras between Frobenius algebras turn the category Frobenius algebras into a Hopf opcategory. We also discuss duality and compatibility results between these structures.
Our theory vastly generalizes the well-known fact that any homomorphism beween Frobenius algebras is an isomorphism, but also allows to go beyond classical (iso)morphisms between Frobenius algebras, especially in finite characteristic, as we show by some explicit examples. The paper is concluded with some open questions and considerations about Topological Quantum Field Theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hopf category of Frobenius algebras Großkopf, Paul Vercruysse, Joost Quantum Algebra Category Theory Rings and Algebras We show that the universal measuring coalgebras between Frobenius algebras turn the category of Frobenius algebras into a Hopf category (in the sense of Batista-Caenepeel-Vercruysse), and the universal comeasuring algebras between Frobenius algebras turn the category Frobenius algebras into a Hopf opcategory. We also discuss duality and compatibility results between these structures. Our theory vastly generalizes the well-known fact that any homomorphism beween Frobenius algebras is an isomorphism, but also allows to go beyond classical (iso)morphisms between Frobenius algebras, especially in finite characteristic, as we show by some explicit examples. The paper is concluded with some open questions and considerations about Topological Quantum Field Theories. |
| title | The Hopf category of Frobenius algebras |
| topic | Quantum Algebra Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2406.18499 |