Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.09427 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910205966548992 |
|---|---|
| author | Campbell, Alexander |
| author_facet | Campbell, Alexander |
| contents | We fix the notion of parity complex by a judicious selection from among the axioms originally considered by Street. We show that parity complexes so defined, together with the morphisms of parity complexes defined by Verity, form a category equivalent to the category of strong Steiner complexes (nés augmented directed complexes with strongly loop-free unital bases). To this end, we isolate the purely combinatorial structure possessed by the bases of free augmented directed complexes. This analysis reveals the essential advantage of Steiner's formalism to be that the role of subsets in Street's formalism is played instead by multisets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity complexes redux Campbell, Alexander Category Theory 18N30 We fix the notion of parity complex by a judicious selection from among the axioms originally considered by Street. We show that parity complexes so defined, together with the morphisms of parity complexes defined by Verity, form a category equivalent to the category of strong Steiner complexes (nés augmented directed complexes with strongly loop-free unital bases). To this end, we isolate the purely combinatorial structure possessed by the bases of free augmented directed complexes. This analysis reveals the essential advantage of Steiner's formalism to be that the role of subsets in Street's formalism is played instead by multisets. |
| title | Parity complexes redux |
| topic | Category Theory 18N30 |
| url | https://arxiv.org/abs/2605.09427 |