Hey Chris,

> They are weird, very useful though. It's part of a general maxim in CS that you start counting at 0. I.e. that you want to include the trivial or even pathological cases.

>

> A empty space with no sand is still a heap of sand, at least in CS.

I've been mulling over how to extend the exponential object construction I read about in the Awodey lecture notes to a any suitable category of \\(\mathcal{V}\\)-enriched category functors.

No matter what \\(\mathcal{V}\\) is, we can define \\((\mathcal{X} \times \mathcal{Y})((a,b),(c,d)) := \mathcal{X}(a,c) \otimes \mathcal{Y}(b,d)\\). In the case of \\(\mathcal{V} = \mathbf{Bool}\\) this is just product orders.

Any ideas what properties \\(\mathcal{V}\\) needs to have to make the set of functors \\(\lbrace F: \mathcal{X} \to \mathcal{Y} \mid F \text{ is a } \mathcal{V}\text{-functor}\rbrace\\) a \\(\mathcal{V}\\)-category?

> They are weird, very useful though. It's part of a general maxim in CS that you start counting at 0. I.e. that you want to include the trivial or even pathological cases.

>

> A empty space with no sand is still a heap of sand, at least in CS.

I've been mulling over how to extend the exponential object construction I read about in the Awodey lecture notes to a any suitable category of \\(\mathcal{V}\\)-enriched category functors.

No matter what \\(\mathcal{V}\\) is, we can define \\((\mathcal{X} \times \mathcal{Y})((a,b),(c,d)) := \mathcal{X}(a,c) \otimes \mathcal{Y}(b,d)\\). In the case of \\(\mathcal{V} = \mathbf{Bool}\\) this is just product orders.

Any ideas what properties \\(\mathcal{V}\\) needs to have to make the set of functors \\(\lbrace F: \mathcal{X} \to \mathcal{Y} \mid F \text{ is a } \mathcal{V}\text{-functor}\rbrace\\) a \\(\mathcal{V}\\)-category?