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Hall algebras of two equivalent extriangulated categories

Shiquan Ruan, Li Wang, Haicheng Zhang (2024)

Czechoslovak Mathematical Journal

For any positive integer $n$ , let $A_{n}$ be a linearly oriented quiver of type $A$ with $n$ vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories $ℳ_{n + 1}$ and $ℱ_{n}$ , where $ℳ_{n + 1}$ and $ℱ_{n}$ are the two extriangulated categories corresponding to the representation category of $A_{n + 1}$ and the morphism category of projective representations of $A_{n}$ , respectively. As a by-product,...

Hardy fields in several variables

Leonardo Pasini (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si estende il concetto di campo di Hardy [Bou], al contesto dei germi di funzioni in più variabili che sono definite su insiemi semi-algebrici [Br.], [D.] e che risultano essere morfismi di categorie lisce [Pal.]. In tale contesto si dimostra che per ogni campo di Hardy di germi di una fissata categoria liscia $\mathcal{C}$ , la sua chiusura algebrica relativa nell'anello $G\,\mathcal{C}$ , di tutti i germi nella stessa categoria liscia, è un campo di Hardy reale chiuso, che è l'unica chiusura reale del campo...

H-Coextensions in the category of compact semigroups.

J.H. Carruth, C.E. Clark (1974)

Semigroup forum

Hecke operators on the $q$ -analogue of group cohomology.

Lee, Min Ho (2001)

Beiträge zur Algebra und Geometrie

Heisenberg algebra and a graphical calculus

Mikhail Khovanov (2014)

Fundamenta Mathematicae

A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of the vector spaces of morphisms between products of generating objects in this category.

Heller's axioms for homotopy theory

Jerome William Hoffman (1996)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Hereditarity of closure operators and injectivity

Gabriele Castellini, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $𝒜$ . It is shown that, if every object of $𝒜$ is a subobject of an $𝒜$ -object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms.