Related papers: Comonadic base change for enriched categories

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…

We give an abstract criterion for pasting pseudofunctors on two subcategories of a category into a pseudofunctor on the whole category. As an application we extend the variance theory of the twisted inverse image $(-)^!$ over schemes to…

Let $\V$ be a symmetric monoidal model category and let $X$ be an object in $\V$. From this we can construct a new symmetric monoidal model category $Sp^{\Sigma}(\V,X)$ of symmetric spectra objects in $\V$ with respect to $X$, together with…

We fix any bicategory $\mathscr{A}$ together with a class of morphisms $\mathbf{W}_{\mathscr{A}}$, such that there is a bicategory of fractions $\mathscr{A}[\mathbf{W}_{\mathscr{A}}^{-1}]$. Given another such pair…

Delta lenses are a kind of morphism between categories which are used to model bidirectional transformations between systems. Classical state-based lenses, also known as very well-behaved lenses, are both algebras for a monad and coalgebras…

We denote the monoidal bicategory of two-sided modules (also called profunctors, bimodules and distributors) between categories by $\mathrm{Mod}$; the tensor product is cartesian product of categories. For a groupoid $\scr{G}$, we study the…

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…

Let $\mathcal C$ be a category with finite colimits, writing its coproduct $+$, and let $(\mathcal D, \otimes)$ be a braided monoidal category. We describe a method of producing a symmetric monoidal category from a lax braided monoidal…

Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the…

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…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

We adapt the notion of an algebraic theory to work in the setting of quasicategories developed recently by Joyal and Lurie. We develop the general theory at some length. We study one extended example in detail: the theory of commutative…

We extend the classical work of Kock on strong and commutative monads, as well as the work of Hyland and Power for 2-monads, in order to define strong and pseudocommutative relative pseudomonads. In order to achieve this, we work in the…

Let $U$ be a strong monoidal functor between monoidal categories. If it has both a left adjoint $L$ and a right adjoint $R$, we show that the pair $(R,L)$ is a linearly distributive functor and $(U,U)\dashv (R,L)$ is a linearly distributive…

We characterize in terms of bicategories actions of monoidal categories to representation categories of algebras. For that purpose we introduce cocycles in any 2-category $\K$ and the category of Tambara modules over a monad $B$ in $\K$. We…

It is known that every monoidal bicategory has an associated braided monoidal category of scalars. In this thesis we show that every monoidal bicategory, which is closed both monoidally and compositionally, can be enriched over the monoidal…

We study the existence of universal measuring comonoids $P(A,B)$ for a pair of monoids $A$, $B$ in a braided monoidal closed category, and the associated enrichment of a category of monoids over the monoidal category of comonoids. In…

In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which…

Adjunctions of two variables generalize the relationship between tensor product and the internal hom functor in a closed monoidal category. For a pair of ordinary adjunctions $(F\dashv U, F'\dashv U')$ conjugation relates natural…

With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…