2025/10/14

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2025-10-14 17:16:54 +0200bitterx(~marko@user/bitterx) (Quit: bitterx)
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2025-10-14 16:22:49 +0200 <ski> no worries. was fun to ponder a bit
2025-10-14 16:22:36 +0200 <ski> ("free" is relative to the target category (monoids, commutative monoids, commutative idempotent monoids, ..), and also to the source category (sets, monoids, ..). "free commutative monoid on a monoid" means we force multiplication to be commutative, generally causing a lot of previously distinct elements to now be identified with each other. the "abelianization" of a monoid)
2025-10-14 16:21:02 +0200tomsmedinghas to go, sorry
2025-10-14 16:20:32 +0200 <ski> "bags/sets are not quite free" -- they are free, just not free *plain* monoids
2025-10-14 16:20:03 +0200 <ski> hmm .. `Map (k0,k1) v -> Map k0 v -> Map k1 v' would be a similar operation
2025-10-14 16:17:58 +0200 <ski> like, how in relational algebra, division of relations is useful to express queries of the form "for all ..., ..."
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2025-10-14 16:17:29 +0200 <ski> it might be useful to want a (lower approximation to) division, wrt this multiplication
2025-10-14 16:17:29 +0200 <tomsmeding> hm, I guess subsets of a very small universe set could have the required very-non-injective property
2025-10-14 16:17:08 +0200 <tomsmeding> yes I know that bags/sets are not quite free
2025-10-14 16:16:47 +0200 <ski> yes
2025-10-14 16:16:46 +0200 <tomsmeding> something which makes a datastructure grow quadratically in size is not something you use very often
2025-10-14 16:16:23 +0200 <tomsmeding> furthermore, for this to be useful as an abstraction, I'd expect the operation to be used more than, say, once in a program
2025-10-14 16:16:19 +0200 <ski> ((finite) bags are free *commutative* monoids. (finite) sets are free *commutative* *idempotent* monoids)
2025-10-14 16:16:15 +0200luna___(~luna@fedora/bittin) ()
2025-10-14 16:15:31 +0200 <ski> mm, right, scratch the "lists"
2025-10-14 16:15:12 +0200 <tomsmeding> even with Sum/Product the maps still grow quadratically
2025-10-14 16:14:57 +0200 <ski> or `Sum a' or `Product a'
2025-10-14 16:14:50 +0200 <tomsmeding> aren't those free and thus very injective?
2025-10-14 16:14:29 +0200 <ski> like, the keys are lists, bags, or sets ?
2025-10-14 16:14:01 +0200 <ski> unless the key monoid is highly non-injective, i guess
2025-10-14 16:13:43 +0200 <tomsmeding> that's not usually what you want in practice
2025-10-14 16:13:42 +0200 <ski> right
2025-10-14 16:13:30 +0200 <tomsmeding> yes, the other problem is that the maps get very big this way
2025-10-14 16:13:25 +0200 <ski> wanting all combinations of the keys in one map, with the keys in the other map
2025-10-14 16:12:57 +0200 <ski> yea .. it kinda has a "tensor feel"
2025-10-14 16:12:30 +0200 <tomsmeding> *originals
2025-10-14 16:12:21 +0200 <tomsmeding> feels a bit far-fetched to me, not least because the result "invents new keys" that were not there in the original
2025-10-14 16:10:58 +0200 <ski> now .. is there a use case for wanting to multiply `Map k v's, given `Monoid k' ?
2025-10-14 16:09:47 +0200 <ski> so you can no longer keep track of a single element per group (monoid))