Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.10152 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913352867905536 |
|---|---|
| author | Hasegawa, Masahito Lechenne, Serge |
| author_facet | Hasegawa, Masahito Lechenne, Serge |
| contents | We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise to a ribbon combinatory algebra. Conversely, From a ribbon combinatory algebra, we can construct a ribbon category with a reflexive object, from which the combinatory algebra can be recovered. To show this, and also to give the equational characterisation of ribbon combinatory algebras, we make use of the internal PRO construction developed in Hasegawa's recent work. Interestingly, we can characterise ribbon combinatory algebras in two different ways: as balanced combinatory algebras with a trace combinator, and as balanced combinatory algebras with duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braids, twists, trace and duality in combinatory algebras Hasegawa, Masahito Lechenne, Serge Logic in Computer Science 03B40 (Primary) 18M15, 68Q55 (Secondary) F.3.2; D.3.1 We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise to a ribbon combinatory algebra. Conversely, From a ribbon combinatory algebra, we can construct a ribbon category with a reflexive object, from which the combinatory algebra can be recovered. To show this, and also to give the equational characterisation of ribbon combinatory algebras, we make use of the internal PRO construction developed in Hasegawa's recent work. Interestingly, we can characterise ribbon combinatory algebras in two different ways: as balanced combinatory algebras with a trace combinator, and as balanced combinatory algebras with duality. |
| title | Braids, twists, trace and duality in combinatory algebras |
| topic | Logic in Computer Science 03B40 (Primary) 18M15, 68Q55 (Secondary) F.3.2; D.3.1 |
| url | https://arxiv.org/abs/2405.10152 |