All Questions
Tagged with quivers ct.category-theory
6
questions
18
votes
1
answer
6k
views
Intersection between category theory and graph theory
I'm a graduate student who has been spending a lot of time working with categories (model categories, derived categories, triangulated categories...) but I used to love graph theory and have always ...
- 25.6k
5
votes
1
answer
495
views
Morita equivalence of acyclic categories
(Crossposted from math.SE.)
Call a category acyclic if only the identity morphisms are invertible and the endomorphism monoid of every object is trivial. Let $C, D$ be two finite acyclic categories. ...
- 114k
3
votes
1
answer
212
views
Pairs of paths with the same source and target
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 ...
- 9,548
3
votes
0
answers
168
views
A conceptual explanation for the Kirchoff matrix theorem in terms of the quiver algebra
On the wikipedia page for the Kirchoff matrix theorem, they state a souped up version of the theorem:
Let $G$ be a finite undirected loopless graph and let us form the square matrix $L$ indexed by the ...
- 7,498
2
votes
0
answers
133
views
How to compute the derived functor of bounded derived categories of hereditary algebra?
Let $\Lambda$ be
a finite dimensional algebra given by the quiver
$$\cdot\leftarrow\cdot\leftarrow\cdot\rightarrow\cdot.$$
It can be view as an triangulated matrix algebra.
$$\Lambda={A\ \ M\choose0\ ...
- 91
1
vote
1
answer
275
views
finitely presented representations
Let Q=(V,E) be a direct graph where V is the set of all its vertices and E denotes the set of all its arrows. $X$ is called a representation of Q by modules if it is a functor from Q to R-Mod. i.e. $X(...
- 141