Library HoTT.Categories.ExponentialLaws
Exponential Laws
We want to have the following as subdirectories/modules, not at top level. Unfortunately, namespacing in Coq is kind-of broken (see, e.g., https://coq.inria.fr/bugs/show_bug.cgi?id=3676), so we don't get the ability to rename subfolders by
Including into other modules.
Laws about the initial category
x⁰ ≅ 1
0ˣ ≅ 0 if x ≠ 0
Laws about the terminal category
x¹ ≅ x
1ˣ ≅ 1
The law that a sum in an exponent is a product
yⁿ⁺ᵐ ≅ yⁿ × yᵐ
The law that exponentiation distributes over product
(y × z)ⁿ ≅ yⁿ × zⁿ