Related papers: Monoidal Adjunctions - Linearity and Duality
We show that the construction due to Leinster and Weber of a generalized Lawvere theory for a familially representable monad on a (co)presheaf category, and the associated ``nerve'' functor from monad algebras to (co)presheaves, have an…
Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…
In this paper, we classify additive closed symmetric monoidal structures on the category of left R-modules by using Watts' theorem. An additive closed symmetric monoidal structure is equivalent to an R-module Lambda_{A,B} equipped with two…
We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric…
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed…
We prove that the category of dg-coalgebras is symmetric monoidal closed and that the category of dg-algebras is enriched, tensored, cotensored and strongly monoidal over that of coalgebras. We apply this formalism to reconstruct several…
For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…
The category of double categories and double functors is equipped with a symmetric closed monoidal structure. For any double category $\mathbb A$, the corresponding internal hom functor $|[ \mathbb A,-]|$ sends a double category $\mathbb B$…
Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$ of characteristic $p>0$ and let $\ell$ be a prime number different from $p$. Let $U\subset G$ be a maximal unipotent subgroup, and let $T$ be a maximal…
We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…
For functors $L:\A\to \B$ and $R:\B\to \A$ between any categories $\A$ and $\B$, a {\em pairing} is defined by maps, natural in $A\in \A$ and $B\in \B$, $$\xymatrix{\Mor_\B (L(A),B) \ar@<0.5ex>[r]^{\alpha} & \Mor_\A…
We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
A duoidal category is a category equipped with two monoidal structures in which one is (op)lax monoidal with respect to the other. In this paper we introduce duoidal $\infty$-categories which are counterparts of duoidal categories in the…
It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally…
We establish a Galois connection between sub-monads of an augmented monad and sub-functors of the forgetful functor from its Eilenberg-Moore category. This connection is given in terms of invariants and stabilizers defined through universal…
We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…
A traced monad is a monad on a traced symmetric monoidal category that lifts the traced symmetric monoidal structure to its Eilenberg-Moore category. A long-standing question has been to provide a characterization of traced monads without…
We consider a closed symmetric monoidal category $\mathcal{M}$. We show that if $I$ is a small category then $\mathcal{M}^I$ is a closed $\mathcal{M}$-module. We rewrite the Yoneda Lemma in the case of monoidal valued functors. We derive an…
For a functor $Q$ from a category $C$ to the category $Pos$ of ordered sets and order-preserving functions, we study liftings of various kind of structures from the base category $C$ to the total(or Grothendieck) category $\int Q$. That…