Greatly enjoyed this one!

Here's my understanding of the gist. Place 4 stones on the floor, and place ONE arrow (e.g. a pen) between any 2 stones. (we'll have placed a total of 6 pens.)

The stones are the “objects” in category theory. The arrows represent the morphisms (or just think of morphism as function). But, since now there is only 1 arrow between any 2 stones, we can relook the whole picture, and now think of the arrow as relation between 2 stones!

So, if S1 → S2, we can think of it as S1 ≥ S2. So, the whole thing, becomes another notion, namely, what mathematicians calls “preorder” in order theory, where, the stones is the set, and each stone is a element.

right John?

Here's my understanding of the gist. Place 4 stones on the floor, and place ONE arrow (e.g. a pen) between any 2 stones. (we'll have placed a total of 6 pens.)

The stones are the “objects” in category theory. The arrows represent the morphisms (or just think of morphism as function). But, since now there is only 1 arrow between any 2 stones, we can relook the whole picture, and now think of the arrow as relation between 2 stones!

So, if S1 → S2, we can think of it as S1 ≥ S2. So, the whole thing, becomes another notion, namely, what mathematicians calls “preorder” in order theory, where, the stones is the set, and each stone is a element.

right John?