Linearly distributive coherence in the absence of units
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911646266425344 |
|---|---|
| author | Demirdilek, Max Reiher, Christian Schweigert, Christoph |
| author_facet | Demirdilek, Max Reiher, Christian Schweigert, Christoph |
| contents | Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories carry two tensor products, with structural morphisms given by associators and distributors relating the two tensor products. In several examples, including Grothendieck--Verdier categories, also known as $\ast$-autonomous categories, these distributors need not be invertible.
We give a self-contained proof that linearly distributive categories without units are coherent, while units may obstruct coherence. With the same techniques, we also establish an analogous coherence result for Frobenius linearly distributive functors without units. These results admit a reformulation in terms of directed paths in associahedra and multiplihedra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linearly distributive coherence in the absence of units Demirdilek, Max Reiher, Christian Schweigert, Christoph Combinatorics Category Theory Quantum Algebra 05C20 (Primary) 18M05, 18N20, 52B05 (Secondary) Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories carry two tensor products, with structural morphisms given by associators and distributors relating the two tensor products. In several examples, including Grothendieck--Verdier categories, also known as $\ast$-autonomous categories, these distributors need not be invertible. We give a self-contained proof that linearly distributive categories without units are coherent, while units may obstruct coherence. With the same techniques, we also establish an analogous coherence result for Frobenius linearly distributive functors without units. These results admit a reformulation in terms of directed paths in associahedra and multiplihedra. |
| title | Linearly distributive coherence in the absence of units |
| topic | Combinatorics Category Theory Quantum Algebra 05C20 (Primary) 18M05, 18N20, 52B05 (Secondary) |
| url | https://arxiv.org/abs/2605.03113 |