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Override and Update in Restriction Categories

  • Jean-Simon Pacaud Lemay
  • Chad Nester
Open at sourcePDFDOICite

Abstract

We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which both of the operators in question exist. We prove a number of results concerning these operators and their relationship to the structure of the ambient restriction category, as well as relating them to the existing literature on the override and update operators. We provide various examples of override restriction categories and in particular show that every classical restriction category is an override restriction category.

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Cite

BibTeXRIS
BibTeX
@misc{lemay2026override,
  title = {{Override and Update in Restriction Categories}},
  author = {Jean-Simon Pacaud Lemay and Chad Nester},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03472},
  eprint = {2609.03472},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03472},
}
RIS
TY  - UNPB
TI  - Override and Update in Restriction Categories
AU  - Jean-Simon Pacaud Lemay
AU  - Chad Nester
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03472
UR  - https://arxiv.org/abs/2609.03472
AB  - We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which both of the operators in question exist. We prove a number of results concerning these operators and their relationship to the structure of the ambient restriction category, as well as relating them to the existing literature on the override and update operators. We provide various examples of override restriction categories and in particular show that every classical restriction category is an override restriction category.
ER  -