Related papers: Gr\"obner Bases for Coloured Operads

In this paper, we study toric ideals associated with multichains of posets. It is shown that the comparability graph of a poset is chordal if and only if there exists a quadratic Gr\"obner basis of the toric ideal of the poset. Strong…

We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function…

We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalized operads (e.g. cyclic operads, modular operads, properads, and so on), and give new, uniform definitions for their morphisms.…

In this paper we unify previous developments on higher operads and multitensors into a single framework in which the interplay between multitensors on a category V, and monads on the category of graphs enriched in V, is taken as…

In this paper, we propose a method for constructing a colored $(d+1)$-operad $\mathbf{seq}_d$ in $\mathrm{Sets}$, in the sense of Batanin [Ba1,2], whose category of colors (=the category of unary operations) is the category $\Theta_d$, dual…

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…

Using the description of enriched $\infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $\infty$-operads as certain modules in symmetric sequences. For $\mathbf{V}$ a symmetric monoidal model…

We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modular operads to presheaves is fully faithful, and its essential…

An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…

Let $K\langle X\rangle =K\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over a field $K$, and let $R\langle X\rangle =R\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over an arbitrary commutative ring…

We introduce an operad of formal fractions, abstracted from the Mould operads and containing both the Dendriform and the Tridendriform operads. We consider the smallest set-operad contained in this operad and containing four specific…

We build model structures on the category of equivariant simplicial operads with weak equivalences determined by families of subgroups, in the context of operads with a varying set of colors (and building on the fixed color model structures…

We define a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type $F_4$. In this way, we obtain a set of…

We introduce balanced polyominoes and show that their ideal of inner minors is a prime ideal and has a quadratic Gr\"obner basis with respect to any monomial order, and we show that any row or column convex and any tree-like polyomino is…

We prove a stabilization theorem for algebras of n-operads in a monoidal model category. It implies a version of Baez-Dolan stabilization hypothesis for Rezk's weak n-categories and some other stabilization results.

We give a framework for comparing on the one hand theories of n-categories that are weakly enriched operadically, and on the other hand n-categories given as algebras for a contractible globular operad. Examples of the former are the…

We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…

The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a…

We build model structures on the category of equivariant simplicial operads with a fixed set of colors, with weak equivalences determined by families of subgroups. In particular, by specifying to the family of graph subgroups (or, more…

In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…