65 citations · 239 across the 22 of their papers we have counts for
27 papers
Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads
Gabriella Böhm
We associate, in a functorial way, a monoidal bicategory to any monoidal bicategory . Two examples of this construction are of particular in…
Weak multiplier bimonoids
Gabriella Böhm, José Goméz-Torrecillas, Stephen Lack
Based on the novel notion of `weakly counital fusion morphism', regular weak multiplier bimonoids in braided monoidal categories are introduced. They generalize weak multiplier bia…
A simplicial approach to multiplier bimonoids
Gabriella Böhm, Stephen Lack
Although multiplier bimonoids in general are not known to correspond to comonoids in any monoidal category, we classify them in terms of maps from the Catalan simplicial set to ano…
Multiplier Hopf monoids
Gabriella B"ohm, Stephen Lack
The notion of multiplier Hopf monoid in any braided monoidal category is introduced as a multiplier bimonoid whose constituent fusion morphisms are isomorphisms. In the category of…
A category of multiplier bimonoids
Gabriella Böhm, Stephen Lack
The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C. Adapting the philosophy of Janssen and Vercruysse, and making some mild assumpti…
Hopf comonads on naturally Frobenius map-monoidales
Gabriella Böhm, Stephen Lack
We study monoidal comonads on a naturally Frobenius map-monoidale in a monoidal bicategory . We regard them as bimonoids in the duoidal hom-category $\mathcal M(M,M…
Multiplier bialgebras in braided monoidal categories
Gabriella Böhm, Stephen Lack
Multiplier bimonoids (or bialgebras) in arbitrary braided monoidal categories are defined. They are shown to possess monoidal categories of comodules and modules. These facts are e…
Weak bimonoids in duoidal categories
Yuanyuan Chen, Gabriella Böhm
Weak bimonoids in duoidal categories are introduced. They provide a common generalization of bimonoids in duoidal categories and of weak bimonoids in braided monoidal categories. U…
Weak multiplier bialgebras
Gabriella Böhm, José Gómez-Torrecillas, Esperanza López-Centella
A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebr…
On the category of weak bialgebras
Gabriella Böhm, José Gómez-Torrecillas, Esperanza López-Centella
Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak…
Firm Frobenius monads and firm Frobenius algebras
Gabriella Böhm, José Gómez-Torrecillas
Firm Frobenius algebras are firm algebras and counital coalgebras such that the comultiplication is a bimodule map. They are investigated by categorical methods based on a study of…
On Hopf monoids in duoidal categories
Gabriella Böhm, Yuanyuan Chen, Liangyun Zhang
Aguiar and Mahajan's bimonoids A in a duoidal category M are studied. Under certain assumptions on M, the Fundamental Theorem of Hopf Modules is shown to hold for A if and only if…
On the double crossed product of weak Hopf algebras
Gabriella Böhm, José Gómez-Torrecillas
Given a weak distributive law between algebras underlying two weak bialgebras, we present sufficient conditions under which the corresponding weak wreath product algebra becomes a…
On the iteration of weak wreath products
Gabriella Böhm
Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any…
Bilinear factorization of algebras
Gabriella Böhm, José Gómez-Torrecillas
We study the (so-called bilinear) factorization problem answered by a weak wreath product (of monads and, more specifically, of algebras over a commutative ring) in the works by St…
Weak bialgebras and monoidal categories
G. Böhm, S. Caenepeel, K. Janssen
We study monoidal structures on the category of (co)modules over a weak bialgebra. Results due to Nill and Szlachányi are unified and extended to infinite algebras. We discuss the…
Idempotent splittings, colimit completion, and weak aspects of the theory of monads
Gabriella Böhm, Stephen Lack, Ross Street
We show that some recent constructions in the literature, named `weak' generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Car…
On the 2-categories of weak distributive laws
Gabriella Böhm, Stephen Lack, Ross Street
A weak mixed distributive law (also called weak entwining structure) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generali…
A categorical approach to cyclic duality
Gabriella Böhm, Dragos Stefan
The aim of this paper is to provide a unifying categorical framework for the many examples of para-(co)cyclic modules arising from Hopf cyclic theory. Functoriality of the coeffici…
Pre-torsors and Galois comodules over mixed distributive laws
Gabriella Böhm, Claudia Menini
We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory o…
Monads and comonads in module categories
Gabriella Böhm, Tomasz Brzezinski, Robert Wisbauer
Let be a ring and $\M_A$ the category of -modules. It is well known in module theory that for any -bimodule , is an -ring if and only if the functor $-\otimes_…
Examples of para-cocyclic objects induced by BD-laws
Gabriella Böhm, Dragos Stefan
In a recent paper arXiv:0705.3190, we gave a general construction of a para-cocyclic structure on a cosimplex, associated to a so called admissible septuple -- consisting of two ca…
Morita theory of comodules over corings
Gabriella Böhm, Joost Vercruysse
By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an equivalence between appropriate subcategories of the module categories of the two rings…
(Co)cyclic (co)homology of bialgebroids: An approach via (co)monads
Gabriella Böhm, Dragos Stefan
For a (co)monad T_l on a category M, an object X in M, and a functor Π: M \to C, there is a (co)simplex Z^*:=ΠT_l^{* +1} X in C. Our aim is to find criteria for para-(co)cyclicity…