In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a more general coinduction functor between categories ...

We describe an explicit crystal morphism between Nakajima monomials and monomials which give a realization of crystal bases for finite dimensional irreducible modules over the quantized enveloping algebra for Lie algebras of type A and C. This morphism provides a connection between arbitrary Nakajima monomials and Kashiwara–Nakashima tableaux. This yields a translation of Nakajima monomials to ...

This morphism sends probability calculus into optimal control problems. Therefore almost of the concepts introduced in probability calculus have an optimization counterpart. The purpose of this paper is to make a presentation of known and new results of optimal control with this morphism in mind. The emphasis of this talk is i) on the trajectory point of view by opposition to the cost point of ...

Let X be a projective scheme over a field. We show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the Frobenius morphism. We also compare various definitions of ample locally free sheaf and show that the vanishing given by the Frobenius morphism is, in a certain sense, the strongest possible. Our work can be viewed as various...

We conjecture an explicit formula for a cyclic analog of the Formality L∞-morphism [K]. We prove that its first Taylor component, the cyclic Hochschild-Kostant-Rosenberg map, is in fact a morphism (and a quasiisomorphism) of the complexes. To prove it we construct a cohomological version of the Connes-Tsygan bicomplex in cyclic homology. As an application of the cyclic Formality conjecture, we ...

We introduce a notion of morphism of CohFT’s, on the basis of the analogy with A∞ morphisms, and discuss the relationship with morphisms of F -manifolds introduced by Manin and Hertling [5]. The structure maps of a morphism of CohFT’s have as input a cohomology class on the moduli space of scaled affine lines (complexified multiplihedron) studied in Ma’u-Woodward [9]. The main result is a compu...

An automatic sequence is a letter-to-letter coding of fixed point uniform morphism. More generally, morphic sequences are codings points arbitrary morphisms. There many examples where an, priori, with non-uniform morphism happens to be an sequence. example the Lysënok \(a \to aca\), \(b d\), \(c b\), \(d c\), which also \(2\)-automatic Such identification useful for describing dynamical systems...

Abstract We investigate several questions related to the notion of recognizable morphism. The main result is a new proof Mossé’s theorem and actually generalization more general class morphisms due Berthé et al [Recognizability for sequences morphisms. Ergod. Th. & Dynam. Sys. 39 (11) (2019), 2896–2931]. prove most morphisms, including ones with erasable letters. Our derived from concerning...

Problem 1. Let C be a category with the zero object OC (that is, an object which is both universal and co-universal). In particular, for any pair of objects M and N , we have a distinguished morphism 0M,N ∈ HomC (M,N) , called the zero morphism, which is the composition of the unique morphisms M → OC and OC → N . Let M and N be objects in C and f ∈ HomC (M,N) . Recall that a kernel of f is a pa...

The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of m...