| ← Index | Next: Paths → |
Recall
Formal definition cited in this section, gathered here for quick reference (full citation in the Bibliography):
- Quiver. Stated verbatim as $Q = (Q_0, Q_1, s, t)$ (AssemSimsonSkowronski2006, Definition 1.1, Ch. II §1 “Quivers and path algebras”): a set of vertices $Q_0$, a set of arrows $Q_1$, and two functions $s, t : Q_1 \to Q_0$ giving each arrow’s source and target.
A quiver is a directed graph: a set of vertices and a set of
directed edges (called arrows) between them. This is the same notion
Mathlib calls Quiver (built here from scratch, following Chapter
0’s “no Mathlib” policy, rather than reusing Mathlib’s). Formally, a
quiver $Q$ consists of:
- a set of vertices $Q_0$,
- a set of arrows $Q_1$,
- two functions $s, t : Q_1 \to Q_0$ giving each arrow’s source and target.
Picture an arrow $\alpha : i \to j$ as a literal arrow drawn from vertex $i$ to vertex $j$; $s(\alpha) = i$ and $t(\alpha) = j$.
Example quiver
Take vertices ${1, 2, 3}$ and arrows
\[\alpha : 1 \to 2, \qquad \beta : 2 \to 3\]References
Full citations in the Bibliography. Formal definitions are gathered in Recall, above.
- Assem, Simson, and Skowroński (AssemSimsonSkowronski2006), Definition 1.1, Ch. II §1 “Quivers and path algebras” — quiver.
- Schiffler (Schiffler2014) — an elementary, textbook-level treatment of the same definition.
| ← Index | Next: Paths → |