# Triangle Order $\leq_{\bigtriangleup}$ in Singular Categories

Research paper by Zhengfang Wang

Indexed on: 24 Oct '14Published on: 24 Oct '14Published in: Mathematics - Representation Theory

#### Abstract

We prove that the triangle order $\leq_{\bigtriangleup}$ in the singular category $D_{sg}(A)$ defines a partial order on the set of isomorphism classes of objects in $D_{sg}(A)$ for a finite-dimensional $k$-algebra $A$.