Related papers: Combinatorial $N_\infty$ operads
The basics of operadic variational formalism is presented which is necessary when modeling the operadic systems. A general gauge theoretic approach to the abstract operads, based on the physical measurements concepts, is justified and…
We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of…
We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ homotopy corresponding to a…
We use Lurie's symmetric monoidal envelope functor to give two new descriptions of $\infty$-operads: as certain symmetric monoidal $\infty$-categories whose underlying symmetric monoidal $\infty$-groupoids are free, and as certain symmetric…
We provide a characterization of those nonmonotonic inference operations C for which C(X) may be described as the set of all logical consequences of X together with some set of additional assumptions S(X) that depends anti-monotonically on…
Using the technique of higher derived brackets developed by Voronov, we construct a homotopy Loday algebra in the sense of Ammar and Poncin associated to any symplectic $2$-manifold. The algebra we obtain has a particularly nice structure,…
We prove that Mann-Robalo's construction of the brane action extends to general coherent $\infty$-operads, with possibly multiple colors and non-contractible spaces of unary operations. This requires to establish two results regarding…
In this paper, we generalize the Dunn-Brinkmeier~additivity theorem, which establishes a weak equivalence $\mathcal{C}_n \otimes \mathcal{C}_m \simeq \mathcal{C}_{n+m}$ for the little cubes operad $\mathcal{C}_n$. We introduce equivariant…
In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…
We give a new categorical approach to the Halmos-von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete…
In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…
We study the indexing systems that correspond to equivariant Steiner and linear isometries operads. When $G$ is a finite abelian group, we prove that a $G$-indexing system is realized by a Steiner operad if and only if it is generated by…
The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra. Adapting a definition of Behrens, we introduce mod 2 homology operations for algebras over this operad and prove these operations account for…
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this…
In this paper we show that any $\infty$-operad is equivalent to the localization of a discrete $\Sigma$-free operad, working in the formalism of dendroidal sets. The key point is defining the root functor of a dendroidal set $X$, a functor…
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…
We study the homotopy derivations of the framed little discs operads, which correspond to the homotopy derivations of the BV2n operads. By extending a result by Willwacher about the homotopy derivations of the en operads we show that the…
In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space $\mathbb{X}$ into a Hilbert space $H,$ as a sequence of integers, extending naturally the usual definition of…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
We show that the operations addition and multiplication on the set $C(\Omega)$ of all real continuous functions on $\Omega\subseteq\mathbb{R}^n$ can be extended to the set $\mathbb{H}(\Omega)$ of all Hausdorff continuous interval functions…