Abstract
We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers (in the sense of [9]), and bilinear pairings as special cases. In this general context, we prove the cancelation from direct sums, and show the existence and uniqueness of decomposition into a sum of indecomposable objects, provided certain assumptions hold. This yields similar results for the special cases just mentioned. Using similar ideas, we also prove a version of Fitting's Lemma for natural transformations between functors.
| Original language | American English |
|---|---|
| Pages (from-to) | 2567-2582 |
| Number of pages | 16 |
| Journal | Communications in Algebra |
| Volume | 44 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2 Jun 2016 |
| Externally published | Yes |
Keywords
- Additive category
- Categorical realization
- Fitting's lemma
- Fitting's property
- Pseudo-abelian category
- Quiver
- Semi-centralizer subring
- Semi-invariant subring
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory