Jesus - yes, there are huge religious wars fought over this arbitrary convention.

I actually prefer the nLab, Wikipedia and Borceaux convention, because a \\(\mathcal{V}\\)-enriched functor from \\(\mathcal{X} \times \mathcal{Y}^{\text{op}}\\) to \\(\mathcal{V}\\) can be reinterpreted as a functor from \\(\mathcal{X}\\) to the so-called **presheaf category** \\(\mathcal{V}^{\mathcal{Y}^{\text{op}}}\\), and that's a good thing. For example, the '\\(\mathcal{V}\\)-enriched Yoneda embedding' is a \\(\mathcal{V}\\)-enriched functor

\[ Y \colon \mathcal{X} \to \mathcal{V}^{\mathcal{X}^{\text{op}}} .\]

However, Fong and Spivak use the convention I'm using here... and that's why I'm using it.

I disagree with a lot of their conventions; luckily, it doesn't really matter much which conventions you use.

I actually prefer the nLab, Wikipedia and Borceaux convention, because a \\(\mathcal{V}\\)-enriched functor from \\(\mathcal{X} \times \mathcal{Y}^{\text{op}}\\) to \\(\mathcal{V}\\) can be reinterpreted as a functor from \\(\mathcal{X}\\) to the so-called **presheaf category** \\(\mathcal{V}^{\mathcal{Y}^{\text{op}}}\\), and that's a good thing. For example, the '\\(\mathcal{V}\\)-enriched Yoneda embedding' is a \\(\mathcal{V}\\)-enriched functor

\[ Y \colon \mathcal{X} \to \mathcal{V}^{\mathcal{X}^{\text{op}}} .\]

However, Fong and Spivak use the convention I'm using here... and that's why I'm using it.

I disagree with a lot of their conventions; luckily, it doesn't really matter much which conventions you use.