Related papers: Butterflies in a Semi-Abelian Context

We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…

It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a "plethory": a monoid in the category of…

We introduce a notion of an integral along a bimonoid homomorphism as a simultaneous generalization of the integral and cointegral of bimonoids. The purpose of this paper is to characterize an existence of a specific integral, called a…

Let $V$ be a M\"{o}bius vertex algebra and $G$ an abelian group of automorphisms of $V$. We construct $P(z)$-tensor product bifunctors for the category of $C_{n}$-cofinite grading-restricted generalized $g$-twisted $V$-modules (without…

We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of…

Dold-Thom functors are generalizations of infinite symmetric products, where integer multiplicities of points are replaced by composable elements of a partial abelian monoid. It is well-known that for any connective homology theory, the…

We consider the localisation of the 2-category of diffeological groupoids at weak equivalences from the perspective of anafunctors, and with this language, prove that the localisation of the 2-category of Lie groupoids is an essentially…

In this paper we introduce a strict monoidal subcategory of the category of matrices, suitable to address a higher representation theoretic analogue of radicals (non-semisimplicity) in ordinary representation theory. We show the extent to…

Entwined modules over cowreaths in a monoidal category are introduced. They can be identified to coalgebras in an appropriate monoidal category. It is investigated when such coalgebras are Frobenius (resp. separable), and when the forgetful…

Using crossed homomorphisms, we show that the category of weak representations (resp. admissible representations) of Lie-Rinehart algebras (resp. Leibniz pairs) is a left module category over the monoidal category of representations of Lie…

A monoidal model category is a model category with a compatible closed monoidal structure. Such things abound in nature; simplicial sets and chain complexes of abelian groups are examples. Given a monoidal model category, one can consider…

By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once…

We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…

We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a $\pi_0$-$\pi_1$ exact sequence associated with a fractor between groupoids internal to a pointed exact category.

Under appropriate conditions, if one picks a commutative algebra A with action of group G in braided monoidal category C, the category of A modules in C obtains a natural crossed G-braided structure. In the case of general commutative…

We show how the notion of intercategory encompasses a wide variety of three-dimensional structures from the literature, notably duoidal categories, monoidal double categories, cubical bicategories, double bicategories and Gray categories.…

We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…

In this article, we develop a notion of Quillen bifibration which combines the two notions of Grothendieck bifibration and of Quillen model structure. In particular, given a bifibration $p:\mathcal E\to\mathcal B$, we describe when a family…

Let $\mathscr{C}_{+}(a,b)$ be the submonoid of the bicyclic monoid which is studied in \cite{Makanjuola-Umar=1997}. We describe monoid endomorphisms of the semigroup $\mathscr{C}_{+}(a,b)$ which are generated by the family of all…

Associated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category…