Related papers: The monoidal centre as a limit
We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.
The category of Hilbert modules may be interpreted as a naive quantum field theory over a base space. Open subsets of the base space are recovered as idempotent subunits, which form a meet-semilattice in any firm braided monoidal category.…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a…
I describe a generalization of the notion of operadic category due to Batanin and Markl. For each such operadic category I describe a skew monoidal category of collections, such that a monoid in this skew monoidal category is precisely an…
One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce…
We study semi-strict tricategories in which the only weakness is in vertical composition. We construct these as categories enriched in the category of bicategories with strict functors, with respect to the cartesian monoidal structure. As…
We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.
Monoidal functors U:C --> M with left adjoints determine, in a universal way, monoids T in the category of oplax monoidal endofunctors on M. Such monads will be called bimonads. Treating bimonads as abstract "quantum groupoids" we derive…
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…
We study some examples of braided categories and quasitriangular Hopf algebras and decide which of them is pseudosymmetric, respectively pseudotriangular. We show also that there exists a universal pseudosymmetric braided category.
We show that every braided monoidal category arises as $\End(I)$ for a weak unit $I$ in an otherwise completely strict monoidal 2-category. This implies a version of Simpson's weak-unit conjecture in dimension 3, namely that one-object…
It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of…
This is the last part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans - crossed…
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 prove Heyneman-Radford Theorem in the framework of Monoidal Categories.
In this paper, we introduce the category of brace triples in a braided monoidal setting and prove that it is isomorphic to the category of s-Hopf braces, which are a generalization of cocommutative Hopf braces. After that, we obtain a…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…