12:16 AM
But the sum of the maxes $\geq$ the max of the sums, amirite?

@MikeMiller I only got 40... I spent too long on a problem, evaluating a sum.

oof :(

This text says "Let $X_i$ be spaces and let $\pi_i : \Pi_i X_i \to X_i$ be the projection." What is the general definition of a "projection?"

the projection $X \times Y \to X$ is the map $(x,y) \mapsto x$
generalize

$\pi_i(a,\dots,d,x_i,e,\dots,f) = x_i$, if I'm not mistaken.
where $x_i \in X_i$.

12:25 AM
Oh, thank you

if you're just talking categorically, though, the product $\prod_i X_i$ has a "projection map" $\pi_j: \prod_i X_i \to X_j$ just as part of the data of the product
in an arbitrary category there's not much reason to believe it relates the notion of projection of a cartesian product of sets

@MikeMiller I'm reading through Lang's Algebra book, and I came across the below- it's really obvious, but I'm blanking on what a good way to show it might be.
It's talking about a commutative monoid.