Weak Cat-Operads

Colored operads, series on colored operads, and combinatorial generating systems

A new sort of combinatorial generating system, called bud generating system, is introduced. Bud generating systems are devices for specifying sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous grammars, allowing to work with all these generating systems in a unified way. The theory of bud generating sy...

Weak Hyperbolization Conjecture for 3-dimensional Cat(0) Groups

In this note we prove a weak hyperbolization conjecture for CAT(0) 3-dimensional Poincaré duality groups.

Operads in algebraic combinatorics

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 algebraically the structures thus obtained (changes of bases, generating sets, presentations, morphisms, representations), to collect combinatorial informatio...

Are Operads Algebraic Theories

I exhibit a pair of non-symmetric operads that, while not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if ‘algebraic theory’ is understood as meaning ‘monad’ then operads cannot be regarded as algebraic theories of a special kind.

Enriched infinity operads