Related papers: Commutative graded monads
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…
We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy…
We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with…
We start from any small strict monoidal braided Ab-category and extend it to a monoidal nonstrict braided Ab-category which contains braided bialgebras. The objects of the original category turn out to be modules for these bialgebras
Indexed symmetric monoidal categories are an important refinement of bicategories -- this structure underlies several familiar bicategories, including the homotopy bicategory of parametrized spectra, and its equivariant and fiberwise…
A traced monad is a monad on a traced symmetric monoidal category that lifts the traced symmetric monoidal structure to its Eilenberg-Moore category. A long-standing question has been to provide a characterization of traced monads without…
We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we…
We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…
Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the…
We extend categorical semantics of monadic programming to reversible computing, by considering monoidal closed dagger categories: the dagger gives reversibility, whereas closure gives higher-order expressivity. We demonstrate that Frobenius…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-dimensional topology. We study a generalization of this notion, namely rigid algebras in an arbitrary monoidal 2-category. Examples of rigid algebras include…
A new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Co\c{s}kun and Eden. These algebras are conic (or quadratic) algebras with the extra restriction that the commutator of any two elements is a…
Working in the framework of $(T, V)$-categories, for a symmetric monoidal closed category $V$ and a (not necessarily cartesian) monad $T$, we present a common account to the study of ordered compact Hausdorff spaces and stably compact…
We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data…
Alain Bruguieres, in his talk [1], announced his work [2] with Alexis Virelizier and the second author which dealt with lifting closed structure on a monoidal category to the category of Eilenberg-Moore algebras for an opmonoidal monad. Our…
We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of…