CatDat

Implication Details

Assumptions: binary products, one-way

Conclusions: thin

Reason: Let $X$ be any object. The swap $\tau : X \times X \to X \times X$ is equal to the identity. It follows that the projections $p_1,p_2 : X \times X \rightrightarrows X$ are the same. And this means that all morphisms $Y \rightrightarrows X$ are the same.