
Why an empty sum is 0 and an empty product 1? - ColinWright
https://www.johndcook.com/blog/2015/04/14/empty-sum-product/
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contravariant
Alternatively you could require that the product of the products of two sets
should be equal to the product of their disjoint union. In particular the
product of any set multiplied with the product of the empty set should remain
the same, hence the product of the empty set is the identity.

This avoids some problems you get when you try to generalise the categorical
the notion of product, as it's not immediately clear (to me anyway) how to get
a category where products correspond to an arbitrary group/monoid product.

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BoiledCabbage
The relevant chapter from 'Category Theory for Programmers.'

[https://bartoszmilewski.com/2015/01/07/products-and-
coproduc...](https://bartoszmilewski.com/2015/01/07/products-and-coproducts/)

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tromp
Because Sum_{i=0}^{k} a_i = a_0 + Sum_{i=1}^{k} a_i.

When k = 0, the left side equals a_0, while the right side equals a_0 plus the
empty sum.

Similarly for products.

