Talk:Quiver (mathematics)

message: Multiplying paths together doesn't sound very well defined, unless Quivers carry a natural structure for multiplying them, which would make them almost identical to categories, except without identity elements.
The multiplication structure is perfectly natural -- it's concatenation.  Observe that there are no commutativity restrictions, so quivers have quite a lot less structure than categories. Gleuschk 22:29, 27 September 2006 (UTC)
replies: text: Well, so in order to avoid further misunderstandings, I'll just replace "composition" by concatenation. - Saibot2 10:44, 15 March 2007 (UTC)
thread_title:  Multiplication 

message: It would be great if someone could include the definition of what a path in a quiver is.
:(Somebody did this, but...) JackSchmidt (talk) 06:40, 20 December 2008 (UTC)
replies: text: Yes. This is fixed. JackSchmidt (talk) 06:41, 20 December 2008 (UTC)
thread_title:  what's a path? 

message: What if K is a ring, not a field? Most of the statements in the article do not seem to require that K be a field...  67.100.217.179 (talk) 11:27, 4 May 2008 (UTC)
replies: text: A lot of it works if K is a artinian semisimple ring, but beyond that most of the classification differs a great deal.  If K is self-injective and noetherian, then there is a nice description of injective and projective objects, but there is no longer any nice theory of gabriel roiter on finite representation type.  If K has finite injective dimension, then work of enochs and herzog gives a reasonable picture of the injective and projective objects for neotherian quivers.  In general though (general ring, general quiver) it is a complete mess. JackSchmidt (talk) 06:40, 20 December 2008 (UTC)
thread_title:  What if K is a ring, not a field? 

message: When the multiplication is defined by concatenation, what is the addition of two paths in the path algebra? Perhaps you can add the explanation in the article. It would help me a lot to understand the definition of a path algebra. Thank you. Wohingenau (talk) 00:00, 5 January 2010 (UTC)
thread_title:  Addition in path algebra? 

message: In this article, I see a lot of statements about quivers which presume knowledge about what a quiver is, but I don't see any definition.
What is the difference between a quiver and a directed multigraph? 
If there is none, why is there a separate article about quivers?
This article seems to be mainly about quiver algebras and quiver representations, so shouln't there be two separate articles about those topics?
Also, "head" and "tail" are undefined - I assume it means "target" and "source" of an edge.
-- 132.231.198.153 (talk) 09:37, 7 December 2011 (UTC)
replies: text: Now fixed. linas (talk) 22:41, 19 August 2012 (UTC)
thread_title:  Where is the definition?! 

message: The last line in this section--'Note that Quiv is the category of presheaves on the opposite category Q^op.'--is confusing.  Given that pre-sheaves on Q^op would be the category of contravariant set-valued functors on Q^op, which are just covariant set valued functors on Q, this convoluted language (i.e. the unnecessary double op) makes it seem like there is an error here.  Was the intention to define Quiv as the category of pre-sheaves on Q (i.e. objects covariant functors Q^op \to Set)?  If that wasn't the case, why not just reverse the arrows on the category Q to make the introduction of the word pre-sheaves seem a little less awful?  — Preceding unsigned comment added by 139.147.60.173 (talk) 14:50, 10 June 2019 (UTC)
thread_title:  Category-theoretic definition