@zanzi Soon, pure functional programming will go the way of the Do . Do bird.

@bgavran @nilesjohnson @Zanzi @hallasurvivor More concretely, the role that W(i) plays in a weighted limit is as an index object for the maps into X(i) - instead of asking for one map from the limit into each X(i), I ask for W(i)-many maps (meaning, a map W(i) --> [A, X(i)]. The functoriality of W tells me how these maps are supposed to be related under postcomposition by the maps in the diagram.

Then if I'm doing a colimit, this is *precomposition*, so the functoriality goes the other way.

@bgavran @nilesjohnson @Zanzi @hallasurvivor The simple explanation is that "colimits are just limits in the opposite category". If I have a diagram X: I --> C and want to compute a limit in C^op, the dual is a diagram I^op --> C^op. So to compute a weighted limit of this, I need a weight on I^op, not on I.

@bgavran @nilesjohnson @Zanzi @hallasurvivor W should be contravariant here, right? (Both to serve as a weight for a colimit, and to make the coend given there non-mute)

Reading a ten-page paper that you know could easily be simplified into 100 pages of category theory

How to win low-rated chess:

- Don't blunder your queen
- Wait until your opponent blunders their queen
- Dude what are you doing
- Dude
- Dude, I told you not to blunder your queen

The word "ungrateful" is redundant. It should just be "grateless"

I still can't get over how stupid "eat out to help out" was

"Why did you dunk-QT me?!" said the frog to the scorpion, "Now both our timelines will be worse!"

The world if the SI people hadn't defined a liter to be roughly two pints.

Small brain: Here's the statement of the theorem, here's the proof.
Medium brain: You can find it in this other paper.
Big brain: The result is folklore, I heard about it from this guy.
Galaxy brain: If you cajole ChatGPT a bit you can get it to give you a proof.

My toxic trait is staying in the yellow on all my beeminder goals so I can use the emergency warnings as reminders.

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a Schelling point for those who seek one