quivers

A quiver is a container for arrows used by archers. It is worn on the hip or carried on the back and designed to keep arrows accessible while protecting them from damage. Quivers come in various shapes and sizes but share common elements: an inner pouch or sleeve to hold arrows, a mounting system to attach the quiver to the body, and often an opening that allows arrows to be drawn smoothly. Materials range from traditional leather and wood to modern plastics. Hip quivers hang at the waist; back quivers rest on the back and offer low profile or balance; bow quivers attach to a bow and keep arrows aligned with the weapon. Some designs include padded interiors, adjustable straps, and quick-release features. Arrow capacity typically ranges from a few to more than two dozen, depending on the archer’s needs and clothing.

In mathematics, a quiver is a directed graph consisting of vertices and arrows. Quivers are central in representation theory and algebraic geometry, where they model relations and linear maps between vector spaces. A representation assigns to each vertex a vector space and to each arrow a linear map between those spaces; morphisms between representations preserve these structures. The path algebra of a quiver encodes compositions of arrows, and quivers with relations impose constraints on those compositions. Dynkin quivers, which are acyclic and of certain types, classify finite-dimensional representations; Gabriel’s theorem links these quivers to simply laced Dynkin diagrams. Quivers also appear in cluster algebras, Hall algebras, and string theory, where mutation and derived categories reveal deeper structure. The term thus denotes both a practical container used in archery and, in mathematics, a tool for studying algebraic objects via directed graphs and their representations.