If C is an abelian category, the category Ind(C) of ind-objects of C has many remarkable properties: it is much bigger than C, it contains C, and furthermore it is dual (in a certain sense) to C. We introduce here the category of ind-sheaves on a locally compact space X as the category of ind-objects of the category of sheaves with compact supports. This construction has some analogy with that ...

The aim of this paper is to develop the coalgebra counterpart of the HomAlgebra notions. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations and giving rise to the class of quasi-Lie algebras incorporating Hom-Lie algebras, we describe the notion and some properties of Homalgebras and provide examples of formal deformations of ...

We define a contravariant functor K· from the category of finite graphs and graph morphisms to the category of finitely generated graded abelian groups and homomorphisms. For a graph X, an abelian group B, and a nonnegative integer j, an element of Hom(K(X), B) is a coherent family of B-valued flows on the set of all graphs obtained by contracting some (j − 1)-set of edges of X; in particular, ...

The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12].

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...

Bicat is the tricategory of bicategories, homomorphisms, pseudonatural transformations, and modifications. Gray is the subtricategory of 2-categories, 2functors, pseudonatural transformations, and modifications. We show that these two tricategories are not triequivalent. 1. Background. Weakening the notion of 2-category by replacing all equations between 1-cells by suitably coherent isomorphism...

Abstract The goal of this paper is to introduce and give some constructions study properties Hom-left-symmetric color dialgebras Hom-tridendriform algebras. Next, we their connection with Hom-associative algebras, Hom-post-Lie algebras Hom–Poisson dialgebras. Finally, generalize Yau’s twisting a class Hom-algebras use endomorphisms or elements centroids produce other from given one.

A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov in [4] and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras in [5, 6]. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic struc...

The genes encoding aspartate kinase (ask), homoserine dehydrogenase (hom), homoserine kinase (thrB) and threonine synthase (thrC) from the obligate methylotroph Methylobacillus flagellatus were cloned. In maxicells hom and thrC directed synthesis of 51 and 48 kDa polypeptides, respectively. The hom, thrB and thrC genes and adjacent DNA areas were sequenced. Of the threonine biosynthesis genes, ...