In this paper we give a new foundational, categorical formulation for operations and
relations and objects parameterizing them. This generalizes and unifies the theory of …

The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic
categories and their operads. This theory is, in our opinion, of an independent value. In Part …

We study the category of algebras of substitudes (also known to be equivalent to the regular
patterns of Getzler and operads coloured by a category) equipped with a (semi) model …

We consider a theory of centers and homotopy centers of monoids in monoidal categories
which themselves are enriched in duoidal categories. The duoidal categories (introduced by …

We introduce two coloured operads in sets–the lattice path operad and a cyclic extension of
it–closely related to iterated loop spaces and to universal operations on cochains. As main …

We prove the equivalence of several hypotheses that have appeared recently in the
literature for studying left Bousfield localization and algebras over a monad. We find …

We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-
category of substitudes of Day and Street (2003), and that the Feynman categories of …

We prove that the operad B of natural operations on the Hochschild cohomology has the
homotopy type of the operad of singular chains on the little disks operad. To achieve this …

We consider three a priori totally different setups for Hopf algebras from number theory,
mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for …

We introduce the notion of n-commutativity (0 Ä n Ä 1) for cosimplicial monoids in a
symmetric monoidal category V, where n D 0 corresponds to just cosimplicial monoids in V …