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Completeness for monads and theories

2021/04/01 by Roman Kositsyn, Kositsyn, Roman
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2104.00367

openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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