A Remark on the Morita Theorem for Operads

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures

     In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from  a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omeg...

Moduli Spaces and Formal Operads

Let Mg,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations that relate the different moduli spaces identifying marked points, the family (Mg,l)g,l is a modular operad of projective smooth Deligne-Mumford stacksM. In this paper, we prove that the modular operad of singular chains S∗(M;Q) is formal, so it is weakly equivalent to the modular operad...

MULTIVARIABLE COCHAIN OPERATIONS AND LITTLE n-CUBES

This paper has two goals. The first (see Theorem 2.15 and Remark 2.16(a)) is to construct a small E∞ chain operad S which acts naturally on the normalized cochains S∗X of a topological space X . This is of interest in view of a theorem of Mandell [15, page 44] which states that if O is any E∞ chain operad over Fp (the algebraic closure of the field with p elements) which acts naturally on S∗X ⊗...

Operads of higher transformations for globular sets and for higher magmas

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...