Categorical Realizations of Quivers

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.

Original languageEnglish
Pages (from-to)2567-2582
Number of pages16
JournalCommunications in Algebra
Volume44
Issue number6
DOIs
StatePublished - 2 Jun 2016
Externally publishedYes

Bibliographical note

Funding Information:
This research was supported by an ERC grant #226135 and by the Lady Davis Fellowship Trust

Publisher Copyright:
© 2016, Copyright © Taylor & Francis Group, LLC.

Keywords

  • Additive category
  • Categorical realization
  • Fitting's lemma
  • Fitting's property
  • Pseudo-abelian category
  • Quiver
  • Semi-centralizer subring
  • Semi-invariant subring

ASJC Scopus subject areas

  • Algebra and Number Theory

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