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 -categories. Additionally, we introduce the notion of complete theories that is unique to the -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 -categorical context.
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