In order to study relative PCF-definability of boolean functions, we associate a hypergraph Hf to any boolean function f (following [2, 4]). We introduce the notion of timed hypergraph morphism and show that it is: – Sound: if there exists a timed morphism from Hf to Hg then f is PCF-definable relatively to g. – Complete for subsequential functions: if f is PCF-definable relatively to g, and g ...

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called “amiable” or “M equivalent”. The presented paper uses the results obtained in [3] for the binary case. The aim is to distinguish the amiable words by using a morphism that provides additional information about...

We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by t...

We present results on multiplicity theory. Differential operators on smooth schemes play a central role in the study of the multiplicity of an embedded hypersurface at a point. This follows from the fact that the multiplicity is defined by the Taylor development of the defining equation at such point. On the other hand, the multiplicity of a hypersurface at a point can be expressed in terms of ...

Every morphism from ℙ n to

We complete and extend the construction of algebraic cobordism from [4]. Let k be a field admitting resolution of singularities, let Schk denote the category of finite type schemes over a field k, and let Smk be the full subcategory of smooth quasiprojective k-schemes. For an l.c.i. morphism f : X → Y of finite type k-schemes, we define a functorial pullback morphism f ∗. With these pull-back m...