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Diagrammatic bases from stratified normalization

  • Stéphane Gaussent
  • Zuan Liu
  • Philippe Malbos
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Abstract

In this article, we introduce a new rewriting method for computing hom-bases of diagrammatic categories. Our approach is based on stratified presentations, obtained by partitioning an equational presentation into strata according to the rewriting behavior of its relations. We establish modularity principles for termination and confluence in stratified rewriting systems with coefficients in a ring. We then introduce a completion procedure that transforms a stratified presentation into a normalized one, in which mixed interactions between successive strata are absorbed into the normalized rewriting rules, thereby inducing modularity of confluence. This leads to a stratified hom-basis theorem for diagrammatic categories. We illustrate the method by applying it to the q-Schur category, for which we construct a new hom-basis.

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Cite

BibTeXRIS
BibTeX
@misc{gaussent2026diagrammatic,
  title = {{Diagrammatic bases from stratified normalization}},
  author = {Stéphane Gaussent and Zuan Liu and Philippe Malbos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36020},
  eprint = {2609.36020},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36020},
}
RIS
TY  - UNPB
TI  - Diagrammatic bases from stratified normalization
AU  - Stéphane Gaussent
AU  - Zuan Liu
AU  - Philippe Malbos
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36020
UR  - https://arxiv.org/abs/2609.36020
AB  - In this article, we introduce a new rewriting method for computing hom-bases of diagrammatic categories. Our approach is based on stratified presentations, obtained by partitioning an equational presentation into strata according to the rewriting behavior of its relations. We establish modularity principles for termination and confluence in stratified rewriting systems with coefficients in a ring. We then introduce a completion procedure that transforms a stratified presentation into a normalized one, in which mixed interactions between successive strata are absorbed into the normalized rewriting rules, thereby inducing modularity of confluence. This leads to a stratified hom-basis theorem for diagrammatic categories. We illustrate the method by applying it to the q-Schur category, for which we construct a new hom-basis.
ER  -