English

Completeness for monads and theories

Category Theory 2021-06-01 v2

Abstract

We generalize the correspondence between theories and monads with arities of arXiv:1101.3064 to \infty-categories. Additionally, we introduce the notion of complete theories that is unique to the \infty-categorical case and provide a completion construction for a certain class of theories. Along the way we also develop the necessary technical material related to the flagged bicategory of correspondences and lax functor in the \infty-categorical context.

Keywords

Cite

@article{arxiv.2104.00367,
  title  = {Completeness for monads and theories},
  author = {Roman Kositsyn},
  journal= {arXiv preprint arXiv:2104.00367},
  year   = {2021}
}

Comments

56 pages, v2: fixed an error in Lemma 5.28., minor improvements elsewhere

R2 v1 2026-06-24T00:46:03.813Z