Related papers: Galois correspondence for augmented monads

We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize…

This paper considers the possible underlying multicategories for a symmetric monoidal category, and shows that, up to canonical and coherent isomorphism, there really is only one. As a result, there is a well-defined forgetful functor from…

We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria…

A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and…

Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure…

Given a monoidal adjunction, we show that the right adjoint induces a braided lax monoidal functor between the corresponding Drinfeld centers provided that certain natural transformations, called projection formula morphisms, are…

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these…

Given a ring object $A$ in a symmetric monoidal category, we investigate what it means for the extension $\mathbb{1}\rightarrow A$ to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur.…

A monad is constructed in the Goguen category of fuzzy sets valued in a unital quantale, which is an analog of the double contravariant powerset monad in the category of sets. With help of this monad it is proved that the Goguen category of…

In this paper we extend a conjecture of Ash and Sinnott relating niveau one Galois representation to the mod p cohomology of congruence subgroups of SL(n,Z) to include Galois representations of higher niveau. We then present computational…

We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good…

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…

In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times S_2\times\cdots\times S_n$, where $S_j$ is…

Let $G$ be an additive finite abelian group and $\Gamma \subset \operatorname{End} (G)$ be a subset of the endomorphism group of $G$. A sequence $S = g_1 \cdot \ldots \cdot g_{\ell}$ over $G$ is a ($\Gamma$-)weighted zero-sum sequence if…

In previous work, the authors constructed and studied a lift of the Galois correspondence to stable homotopy categories. In particular, if $L/k$ is a finite Galois extension of fields with Galois group $G$, there is a functor $c_{L/k}^*$…

We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre…

We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

We associate two linear categories with two objects to a module over the subalgebra of coinvariants of a Hopf-Galois extension, and prove that they are isomorphic. The structure Theorem for cleft extensions, and the Militaru \cStefan…

We develop an algebraic underpinning of backtracking monad transformers in the general setting of monoidal categories. As our main technical device, we introduce Eilenberg--Moore monoids, which combine monoids with algebras for strong…