Interacting Monoidal Structures with Applications in Computing
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910686735499264 |
|---|---|
| author | Cranch, James Struth, Georg |
| author_facet | Cranch, James Struth, Georg |
| contents | With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of examples for these structures from various domains, including a categorical model for a communication protocol and a lax $n$-fold relational monoid, which has previously been used implicitly for higher-dimensional rewriting and which specialises in a natural way to strict $n$-categories. A special set of examples is built around modules and algebras of the boolean semiring, which allows us to deal with semilattices, additively idempotent semirings and quantales using tools from classical algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interacting Monoidal Structures with Applications in Computing Cranch, James Struth, Georg Category Theory Logic in Computer Science 18D10, 68Q85, 06A12 With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of examples for these structures from various domains, including a categorical model for a communication protocol and a lax $n$-fold relational monoid, which has previously been used implicitly for higher-dimensional rewriting and which specialises in a natural way to strict $n$-categories. A special set of examples is built around modules and algebras of the boolean semiring, which allows us to deal with semilattices, additively idempotent semirings and quantales using tools from classical algebra. |
| title | Interacting Monoidal Structures with Applications in Computing |
| topic | Category Theory Logic in Computer Science 18D10, 68Q85, 06A12 |
| url | https://arxiv.org/abs/2411.03821 |