Related papers: Operads, clones, and distributive laws

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a…

We extend the previous paper "Macdonald's evaluation ... and applications" to the non-symmetric polynomilas recently introduced by Macdonald (as difference counterparts of Opdam's non-symmetric ones).

In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…

The purpose of this foundational paper is to introduce various notions and constructions in order to develop the homotopy theory for differential graded operads over any ring. The main new idea is to consider the action of the symmetric…

We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad…

We show that braided, sylleptic and symmetric monoidal bicategories are precisely the $\mathsf{E}_k$-monoids in the cartesian monoidal $(\infty,1)$-category of bicategories for respective integers $k$. To manage the underlying computations,…

We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representation theory to describe three cyclic and seven dihedral…

We study 2-monads and their algebras using a Cat-enriched version of Quillen model categories, emphasizing the parallels between the homotopical and 2-categorical points of view. Every 2-category with finite limits and colimits has a…

In the paper "Triangulations, orientals, and skew monoidal categories", the free monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk, and so of the free skew…

These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…

We provide a bicategorical generalization of Barr's landmark 1970 paper, in which he describes how to extend Set-monads to relations and uses this to characterize topological spaces as the relational algebras of the ultrafilter monad. With…

Generalized multicategories, also called $T$-monoids, are well known class of mathematical structures, which include diverse set of examples. In this paper we construct a generalization of the adjunction between strict monoidal categories…

We introduce a general definition for colored cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from colored cyclic operads to colored operads has both adjoints, each of…

This paper argues that non-self-adjoint operators can be observables. There are only four ways for this to occur: non-self-adjoint observables can either be normal operators, or be symmetric, or have a real spectrum, or have none of these…

It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The…

We define biprops as a generalization of coloured props and of symmetric weak multicategories. These are bicategories whose objects form a free monoid. They are equipped with some structure resembling a symmetric strict tensor product. We…

It is well known that the forgetful functor from symmetric operads to nonsymmetric operads has a left adjoint $Sym_1$ given by product with the symmetric group operad. It is also well known that this functor does not affect the category of…

We study the existence and left properness of transferred model structures for "monoid-like" objects in monoidal model categories. These include genuine monoids, but also all kinds of operads as for instance symmetric, cyclic, modular,…

We initiate the investigation of representation theory of non-orientable surfaces. As a first step towards finding an additive categorification of Dupont and Palesi's quasi-cluster algebras associated marked non-orientable surfaces, we…

We generalize the classical operad pair theory to a new model for $E_\infty$ ring spaces, which we call ring operad theory, and establish a connection with the classical operad pair theory, allowing the classical multiplicative infinite…