Bartosz Milewski on Nostr: It's possible to define a "proportional product" of two objects using copowers. Given ...
It's possible to define a "proportional product" of two objects using copowers. Given two sets \(A\) and \(B\) we can define \(A \cdot a \times B \cdot b\)
\[ C(A \cdot a \times B \cdot b, c) \cong Set (A, C(a, c)) \times Set(B, C(b, c)\]
I thought of this trying to work out a category theory of French sauces. You need such a product when you mix ingredients in different proportions. I think of a sauce as a functor.
\[ C(A \cdot a \times B \cdot b, c) \cong Set (A, C(a, c)) \times Set(B, C(b, c)\]
I thought of this trying to work out a category theory of French sauces. You need such a product when you mix ingredients in different proportions. I think of a sauce as a functor.