Completeness for monads and theories

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.

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

References in corpus (3)

• Higher Topos Theory
• Gray tensor products and lax functors of $(\infty ,2)$-categories
• Fibrations and lax limits of $(\infty ,2)$-categories

Cited by in corpus (1)

• Factorization systems in $\infty$-categories