Related papers: Enriched Kleisli objects for pseudomonads

In this paper we investigate the categories of braided objects, algebras and bialgebras in a given monoidal category, some pairs of adjoint functors between them and their relations. In particular we construct a braided primitive functor…

Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…

Given a right adjoint functor between triangulated categories and an object in the target category, we show that the unit map of adjunction on that object is a split monomorphism if and only if the object belongs to the additive closure of…

This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…

Consider a monoidal category which is at the same time abelian with enough projectives and such that projectives are flat on the right. We show that there is a $B_{\infty}$-algebra which is $A_{\infty}$-quasi-isomorphic to the derived…

Suppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $\mathcal{E}$ with enough flat projectives, such as the category of complete bornological spaces $\textbf{CBorn}_k$ or the category of inductive limits of…

The notion of a weak duality involution on a bicategory was recently introduced by Shulman in [arXiv:1606.05058]. We construct a weak duality involution on the fully dualisable part of $\text{Alg}$, the Morita bicategory of…

Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…

We introduce a general construction on 2-monads. We develop background on maps of 2-monads, their left semi-algebras, and colimits in 2-category. Then, we introduce the construction of a colimit induced by a map of 2-monads, show that we…

We derive the Christoffel-Geronimus-Uvarov transformations of a system of bi-orthogonal polynomials and associated functions on the unit circle, that is to say the modification of the system corresponding to a rational modification of the…

In this paper we introduce sigma limits (which we write $\sigma$-limits), a concept that interpolates between lax and pseudolimits: for a fixed family $\Sigma$ of arrows of a 2-category $\mathcal{A}$, a $\sigma$-cone for a $2$-functor…

The category of weight modules $L_k(\mathfrak{sl}_2)\text{-wtmod}$ of the simple affine vertex algebra of $\mathfrak{sl}_2$ at an admissible level $k$ is neither finite nor semisimple and modules are usually not lower-bounded and have…

Grothendieck develops the theory of pro-objects over a category $\mathsf{C}$. The fundamental property of the category $\mathsf{Pro}(\mathsf{C})$ is that there is an embedding $\mathsf{C} \overset{c}{\longrightarrow}…

We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids -- or in a straightforward generalisation, the…

We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dg- and…

Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…

Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…

We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external…

We prove a bicategorical analogue of Quillen's Theorem A. As an application, we deduce the well-known result that a pseudofunctor is a biequivalence if and only if it is essentially surjective on objects, essentially full on 1-cells, and…

We collect some isomorphisms of categories and bijections of structures using the Kleisli and Eilenberg-Moore 2-adjunctions.