Return to Question

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.

General diagrams - in categories resp. category theory - do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers?
Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.

General diagrams - in categories resp. category theory - do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers?
Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.

In categories - resp. category theory - general diagrams do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers?
Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.

General diagrams - in categories resp. category theory - do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers?
Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.

Commutative diagrams usually express path equivalences in categories and thus involve pairs of paths in a category with the same source and target.

In categories - resp. category theory - general diagrams do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers? Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.

In categories - resp. category theory - general diagrams do not necessarily involve pairs of paths with the same source and target.

But is there a name for pairs of paths with the same source and target in quivers?
Pairs which only eventually are to be called "commutative" (expressing equivalence)?
("Diagram" would be a badly chosen name.)

The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for "commutative polygons" gave only 10 hits.

Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?

If there is no established name, I would appreciate any suggestion.