The specific statement of Eilenberg swindle Here is Eilenberg-Mazur Swindle in wikipedia, it only gives some examples about the use of Eilenberg swindle. Is there a specific statement of Eilenberg swindle? I want to know the specific statement of Eilenberg swindle for the following question: Let $C$ be a category with infinite direct sum. Suppose $A,B \in obj(C)$ . $L := B \oplus A \oplus B \oplus A \oplus \cdots$, could we have that $A \oplus L \cong L$?

We have $L \cong A^{\oplus \mathbb{N}} \oplus B^{\oplus \mathbb{N}}$ and $A \oplus A^{\mathbb{N}} \cong A^{\mathbb{N}}$, so $A \oplus L \cong L$.