Related papers: Monads on dagger categories

An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality…

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 endow twisted tensor products with a natural notion of counit and comultiplication, and we provide sufficient and necessary conditions making the twisted tensor product a counital coassociative coalgebra. We then characterize when the…

Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss…

This paper answeres the question posed by E.Manes in his book "Algebraic theories": given monoids M and N considered as categories with a single object, and a morphism f: M --> N of monoids (considered as functor), such that f has an…

We prove that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in…

We prove a gluing theorem on the automorphic side of the geometric Langlands correspondence: roughly speaking, we show that the difference between $\mathrm{DMod}(\mathrm{Bun}_G)$ and its full subcategory…

In this article, we prove an isomorphism theorem for the case of refinement $\Gamma$-monoids. Based on this we show a version of the well-known Jordan-H\"older theorem in this framework. The main theorem of this article states that - as in…

Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct…

We study monoids equipped with a second binary operation that captures the structure of the endomorphisms of an object $X$ such that $X=X\times X$. We construct a universal monoid of this type and examine some of its rich combinatorial…

Given a programming language, can we give a monadic denotational semantics that is stable under language extension? Models containing only a single monad are not stable. Models based on type-and-effect systems, in which there is a monad for…

Tangent categories provide a categorical axiomatization of the tangent bundle. There are many interesting examples and applications of tangent categories in a variety of areas such as differential geometry, algebraic geometry, algebra, and…

We study Galois extensions Coinv(M)<M for M an H-comodule algebra and H a Frobenius Hopf algebroid. We obtain generalizations of various theorems in Hopf-Galois theory by Kreimer-Takeuchi, Doi-Takeuchi and Cohen-Fischman-Montgomery. An…

We introduce discrete equational theories where operations are induced by those having discrete arities. We characterize the corresponding monads as monads preserving surjections. Using it, we prove Birkhoff type theorems for categories of…

We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive integer $N$, there are finitely many modular fusion categories…

Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a {\em Morita context} comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is…

The problem of determining gauge and monoidal equivalence classes of fusion categories is considered from the perspective of geometric invariant theory. It is shown that the gauge (or monoidal) class of a fusion category is determined by…

We introduce a framework for universal algebra in categories of relational structures given by finitary relational signatures and finitary or infinitary Horn theories, with the arity $\lambda$ of a Horn theory understood as a strict upper…

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence…