Operads of higher transformations for globular sets and for higher magmas

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 of...

$omega$-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...

Higher Operads, Higher Categories

$omega$-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 $omega$-op...

Steps toward the weak higher category of weak higher categories in the globular setting

We start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{Cambat}. As in cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{N}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. The last chapter of this article asserts that, up to precise...

The Eckman - Hilton argument and higher operads

To the memory of my father. Abstract The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the commutativity of the higher homotopy groups. A reformulation of this argument in the language of higher categories is: suppo...