This paper deals with questions relating to Haghverdi and Scott’s notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully embedded in a totally traced category. Also conversely, every symmetric monoidal subcategory of a totally traced category is partially traced, so this characterize...

With the formal study of natural languages, we have obtained some residual results which greatly increase our power of logical manipulation. Coupled with a computer, our language extends enormously the external logic of our computing device. This paper is concerned with a well-defined symbolic list processing language and a set of operators for this language. These operators, which we call morp...

We introduce a notion of morphism of CohFT algebras, based on the analogy with A∞ morphisms. We outline the construction of a “quantization” of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a Gvariety to the quantum cohomology of its geometric invariant theory or symplectic quotient, and an example relating to the orbifold quantum cohom...

New representation results for three families of regular languages are stated, using a special kind of shuue operation, namely the synchronized shuue. First, it is proved that the family of regular star languages is the smallest family containing the language (a + bc) and closed under synchronized shuue and length preserving morphism. The second representation result states that the family of "...

We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular morphism with connected affine source can be factored into a smooth morphism, a ground-field extension and a generic-fibre embedding. Every variety of characteri...

The purpose of this paper is to study in greater detail the arithmetic KodairaSpencer morphism of an elliptic curve introduced in [Mzk1], Chapter IX, in the general context of the Hodge-Arakelov theory of elliptic curves, developed in [Mzk1-3]. In particular, after correcting a minor error (cf. Corollary 1.6) in the construction of this arithmetic Kodaira-Spencer morphism in [Mzk1], Chapter IX,...

Kontsevich’s formality theorem and the consequent star-product formula rely on the construction of an L∞-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential grade...

It is well-known that any morphism between two p-compact groups will lift, nonuniquely, to an admissible morphism between the maximal tori. We identify here a class of pcompact group morphisms, the p-toric morphisms, which can be perceived as generalized rational isomorphisms, enjoying the stronger property of lifting uniquely to a morphism between the maximal torus normalizers. We investigate ...

In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This phenomena appears in the case when we are using the Second-Order tuple-generating dependencies (SOtgd) with existentially quantified non-built-in functions, for th...

New representation results for three families of regular languages are stated, using a special kind of shuffle operation, namely the synchronized shuffle. First, it is proved that the family of regular star languages is the smallest family containing the language (a+ bc)∗ and closed under synchronized shuffle and length preserving morphism. The second representation result states that the famil...