Non-linear contexts and dependent operads

@misc{cherradi2026nonlinear,
  title = {{Non-linear contexts and dependent operads}},
  author = {El Mehdi Cherradi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39597},
  eprint = {2610.39597},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39597},
}

TY  - UNPB
TI  - Non-linear contexts and dependent operads
AU  - El Mehdi Cherradi
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39597
UR  - https://arxiv.org/abs/2610.39597
AB  - We study the category Dep_aff of finite posets and opfibrations between them, and prove that it is a perfect operator category in the sense of Barwick. Based on its additional properties, we propose a definition for a dependent operator category, and formulate a notion of dependent affine operad in a fibered way. In the particular case of Dep_aff, we investigate the basic theory of such operads, establishing that the category of algebras for an operad is monadic over a canonical presheaf topos of "dependent sets". We finally extend this theory to a setting where we allow variable duplication, which we refer to as general dependent operads.
ER  -