It's possible to define a "proportional product" of two objects using copowers. Given two sets \(A\) and \(B\) we can define \(A \cdot a \times B \cdot b\) using the adjunction:
\[ C(A \cdot a \times B \cdot b, c) \cong Set (A, C(a, c)) \times Set(B, C(b, c))\]
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.
Bartosz Milewski
npub1gl…xtqzy
2025-02-22 13:40:02 UTC
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