Related papers: Protoperads i: Combinatorics and definitions

This paper studies the homotopy theory of the Grothendieck construction using model categories and semi-model categories, provides a unifying framework for the homotopy theory of operads and their algebras and modules, and uses this…

We study a functorial construction from the category of monoids to the category of set-operads and we give some combinatorial examples of applications.

This is an expository article about operads in homotopy theory written as a chapter for an upcoming book. It concentrates on what the author views as the basic topics in the homotopy theory of operadic algebras: the definition of operads,…

We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in…

We establish a combinatorial model for the Boardman--Vogt tensor product of several absolutely free operads, that is free symmetric operads that are also free as $\mathbb{S}$-modules. Our results imply that such a tensor product is always 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…

A new anticyclic operad Mould is introduced, on spaces of functions in several variables. It is proved that the Dendriform operad is an anticyclic suboperad of this operad. Many operations on the free Mould algebra on one generator are…

The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying…

This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…

This work addresses the homotopical analysis of enveloping operads in a general cofibrantly generated symmetric monoidal model category. We show the potential of this analysis by obtaining, in a uniform way, several central results…

Noncommutative multi-indices are noncommutative monomials in a $\mathbb{N}$-indexed family of indeterminates. We define on them a $\mathbb{Z}$-graded operadic structure, with the help of a shifting derivation. Multi-indices of degree 0 are…

Completeness proofs in categorical semantics usually proceed by building a syntactic category whose composition is given by substitution. For untyped effectful Call-by-Value languages, this runs into a basic obstacle: there is no canonical…

We consider the composition product of symmetric sequences in the case where the underlying symmetric monoidal structure does not commute with coproducts. Even though this composition product is not a monoidal structure on symmetric…

Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of…

For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a class of short polytopes the constructed operads are Koszul…

This work studies collections of Hilbert space operators which possess a strict monoid structure under composition. These collections can be thought of as discrete unital semigroups for which no subset of the collection is closed under…

We present the new combinatorial class of product-coproduct prographs which are planar assemblies of two types of operators: products having two inputs and a single output and coproducts having a single input and two outputs. We show that…

Let M be a bicomplete, closed symmetric monoidal category. Let P be an operad in M, i.e., a monoid in the category of symmetric sequences of objects in M, with its composition monoidal structure. Let R be a P-co-ring, i.e., a comonoid in…

We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and…

There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…