@amy > canon compliant
@zanzi Soon, pure functional programming will go the way of the Do . Do bird.
@julesh Holy shit lmao
@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)
@moultano How were these generated?
Applied algebraic abstractologist. Trying to get the heavens into my head.
"Elsk – og berik med drøm – alt stort som var!
Gå mot det ukjente, fravrist det svar!"