The paper extends condensation theory for higher symmetries from fusion n-categories to arbitrary enriched monoidal ∞-categories, using monoidal Eilenberg-Moore functors and iterated module categories.
On lax transformations, adjunctions, and monads in $(\infty,2)$-categories
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We use the basic expected properties of the Gray tensor product of $(\infty,2)$-categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we identify lax transformations between adjunctions and monads with commutative squares of (monadic) right adjoints. We also identify the colax transformations whose components are equivalences (generalizing the "icons" of Lack) with the 2-morphisms that arise from viewing $(\infty,2)$-categories as simplicial $\infty$-categories. Using this characterization we identify the $\infty$-category of monads on a fixed object and colax morphisms between them with the $\infty$-category of associative algebras in endomorphisms.
fields
math.CT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Large condensation in enriched $\infty$-categories
The paper extends condensation theory for higher symmetries from fusion n-categories to arbitrary enriched monoidal ∞-categories, using monoidal Eilenberg-Moore functors and iterated module categories.