The operad that co-represents enrichment

Operad Bimodule Characterization of Enrichment. V2

In a recent talk at CT06 http://faculty.tnstate.edu/sforcey/ct06.htm and in a research proposal at http://faculty.tnstate.edu/sforcey/class_home/research.htm a definition of weak enrichment over a strict monoidal n-category is introduced. We would like to generalize the definition of enrichment in a way which fits naturally into the world of weakened category theory, where multiplication and co...

On a Hopf operad containing the Poisson operad

A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by generators and relations which have some similarity with the Arnold relations for the cohomology of the type A hyperplane arrangement. A map from the operad Ram to t...

The Milgram Non-operad

The anticyclic operad of moulds

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 introduced and studied. Under some restrictions, a forgetful map from moulds to formal vector fields is then defined. A connection to the theory of tilting modul...

The Lattice Path Operad And

We introduce two coloured operads in sets – the lattice path op-erad and a cyclic extension of it – closely related to iterated loop spaces and to universal operations on cochains. As main application we present a formal construction of an E 2-action (resp. framed E 2-action) on the Hochschild cochain complex of an associative (resp. symmetric Frobenius) algebra.