Related papers: Enriched Kleisli objects for pseudomonads

We describe free rigid commutative algebras in $2$-presentably symmetric monoidal $(\infty,2)$-categories as oplax colimits over the $1$-dimensional framed cobordism category. The special case of the $(\infty,2)$-category…

The monoid of multipliers of a semigroup object in a monoidal category is introduced, arising from an abstraction of the definition of the translational hull of an ordinary semigroup or of the multiplier algebra of a Banach algebra and…

In this article the 2-adjunction that relates universal arrows and extensive monads is constructed explicitly. This 2-adjunction resembles the one that relates adjunctions and monads since the 2-category of universal arrows is isomorphic to…

We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…

We introduce dicodensity monads: a generalisation of pointwise codensity monads generated by functors to monads generated by mixed-variant bifunctors. Our construction is based on the notion of strong dinaturality (also known as Barr…

We show that, if S is a finite semiring, then the free profinite S-semimodule on a Boolean Stone space X is isomorphic to the algebra of all S-valued measures on X, which are finitely additive maps from the Boolean algebra of clopens of X…

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal…

The quantum Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial closure is also typical for 2nd order superintegrable…

We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category $\mathcal V$ admitting certain limits. When $\mathcal V$ is equipped with the trivial model structure this recaptures the enriched…

Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple…

This paper extends the theory of universal measuring comonoids to modules and comodules in braided monoidal categories. We generalise the universal measuring comodule Q(M,N), originally introduced for modules over k-algebras when k is a…

Let M be a bicomplete, closed symmetric monoidal category. Let P be an operad in M, i.e., a monoid in the category of symmetric sequences of objects in M, with its composition monoidal structure. Let R be a P-co-ring, i.e., a comonoid in…

For any k-coalgebra C it is shown that similar quasi-finite C-comodules have strongly equivalent coendomorphism coalgebras; (the converse is in general not true). As an application we give a general result about codepth two coalgebra…

A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this note, Mitchell's embedding theorem for a tame schemoid is established. The result allows us to give a cofibrantly generated model…

Let $\mathcal{A}$ and $\mathcal{B}$ be monoidal categories and let $R:\mathcal{A} \rightarrow \mathcal{B}$ be a lax monoidal functor. If $R$ has a left adjoint $L$, it is well-known that the two adjoints induce functors $\overline{R}={\sf…

A fundamental result in the theory of monads is the characterisation of the category of algebras for a monad in terms of a pullback of the category of presheaves on the category of free algebras: intuitively, this expresses that every…

In this paper I develop categorical foundations needed for a rigorous approach to the definition of conformal field theory outlined by Graeme Segal. I discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits,…

Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to G. M. Kelly in the 1960s that there is a very close connection between…

Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…

We introduce and study the Scott adjunction, relating accessible categories with directed colimits to topoi. Our focus is twofold, we study both its applications to formal model theory and its geometric interpretation. From the geometric…