相关论文: Corelations are the prop for extraspecial commutat…

Let $\mathcal C$ be a category with finite colimits, and let $(\mathcal E,\mathcal M)$ be a factorisation system on $\mathcal C$ with $\mathcal M$ stable under pushouts. Writing $\mathcal C;\mathcal M^{\mathrm{op}}$ for the symmetric…

The construction of a category of spans can be made in some categories $\CC$ which do not have pullbacks in the traditional sense. The PROP for monoids is a good example of such a $\CC$. The 2012 book concerning homological algebra by Marco…

If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has developed a theory of "decorated" cospans,…

We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in correspondence with data that can be characterized in terms of…

We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads…

In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar…

We investigate Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads to a…

A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…

The category of all monads over many-sorted sets (and over other "set-like" categories) is proved to have coequalizers and strong cointersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms…

To any bimodule which is finitely generated and projective on one side one can associate a coring, known as a comatrix coring. A new description of comatrix corings in terms of data reminiscent of a Morita context is given. It is also…

We prove Steinebrunner's conjecture on the biequivalence between (colored) properads and labelled cospan categories. The main part of the work is to establish a 1-categorical, strict version of the conjecture, showing that the category of…

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

The category of involutive non-commutative sets encodes the structure of an involution compatible with a (co)associative (co)multiplication. We prove that the category of involutive bimonoids in a symmetric monoidal category is equivalent…

We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of…

It is well known that the category of finite sets and cospans, composed by pushout, contains the universal {\em special} commutative Frobenius algebra. In this note we observe that the same construction yields also general commutative…

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…

We study adjoint and Frobenius pairs of functors, equivalences, and the Picard group for corings.

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

A relationship between coseparable corings and separable non-unital rings is established. In particular it is shown that an A-coring C has an associative A-balanced product. A Morita context is constructed for a coseparable coring with a…

This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…