# Question about the top of a bound representation of a bound quiver.

I am reading the book Elements of the Representation Theory of Associative Algebras: Volume 1.

I have a on page 77. In (d) of Lemma 2.2 on Page 77, it is said that $$L_a=\sum_{\alpha: a\to b} \operatorname{Coker}(\psi_{\alpha}: M_b \to M_a).$$

I think that $L_a$ should be $$L_a=\cap_{\alpha: a\to b} \operatorname{Coker}(\varphi_{\alpha}: M_b \to M_a).$$

Is this true? Thank you very much.

• Do you mean cokernel? – Jim Apr 28 '13 at 7:18
• @Jim, yes. I will edit. – LJR Apr 28 '13 at 7:20

In this case what they mean is that $L_a = M_a/J_a$ where $J_a$ is defined in (c).