We apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our results is the complete classification of simple transitive birepresentations of a bicategory studied in [Zi], which confirms a conjecture made therein.
We apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our results is the complete classification of simple transitive birepresentations of a bicategory studied previously by Zimmermann. The classification confirms a conjecture he has made.
Abstract.Quiver representations arise naturally in the study of representation theory for associative algebras. A particularly simple case to consider is that of representations of finite acyclic quivers, which is the object of study of this thesis. In this thesis we give an explicit presentation of some elementary constructions in the category of quiver representations, which then allows us to formulate and discuss some basic homological algebra within that category. The tools of homological algebra can then be applied to study the canonical problem of representation theory: classification of the indecomposable representations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.