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2021-03-21 18:57:49 × ph88 quits (~ph88@2a02:8109:9e00:7e5c:d4b6:e9e6:3cda:8e26) (Ping timeout: 265 seconds)
2021-03-21 18:58:00 × motersen quits (~user@2001-4dd1-d88a-0-5338-d0f4-6eda-2a0f.ipv6dyn.netcologne.de) (Client Quit)
2021-03-21 18:59:29 × jb55 quits (~jb55@gateway/tor-sasl/jb55) (Ping timeout: 268 seconds)
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2021-03-21 19:00:33 Gurkenglas joins (~Gurkengla@unaffiliated/gurkenglas)
2021-03-21 19:00:41 <joel135> Isn't it remarkable that both exact sequences a -> b -> c and spans defining products u <- (u, v) -> v have the product-like thing in the middle? I didn't notice this explicitly before.
2021-03-21 19:01:34 <unyu> Do you mean 0 -> A -> B -> C -> 0 ?
2021-03-21 19:01:44 jb55 joins (~jb55@gateway/tor-sasl/jb55)
2021-03-21 19:01:53 <unyu> (Feel free to replace 0 with 1 if you are in Grp rather than Ab.)
2021-03-21 19:02:09 motersen joins (~user@2001-4dd1-d88a-0-5338-d0f4-6eda-2a0f.ipv6dyn.netcologne.de)
2021-03-21 19:02:32 <joel135> Oh yes
2021-03-21 19:02:35 × Chai-T-Rex quits (~ChaiTRex@gateway/tor-sasl/chaitrex) (Remote host closed the connection)
2021-03-21 19:02:46 <joel135> I don't actually know homological algebra...
2021-03-21 19:02:47 <unyu> Also, the roles of A and C are not symmetric.
2021-03-21 19:03:09 × minoru_shiraeesh quits (~shiraeesh@109.166.57.171) (Read error: Connection reset by peer)
2021-03-21 19:03:09 Chai-T-Rex joins (~ChaiTRex@gateway/tor-sasl/chaitrex)
2021-03-21 19:03:20 × berberman_ quits (~berberman@unaffiliated/berberman) (Ping timeout: 240 seconds)
2021-03-21 19:03:27 <joel135> Really?
2021-03-21 19:03:29 berberman joins (~berberman@unaffiliated/berberman)
2021-03-21 19:03:51 <unyu> Yep. So the similarities end there.
2021-03-21 19:04:54 <joel135> They at least become each other when you interpret arrows in the opposite category.
2021-03-21 19:04:56 × malumore quits (~malumore@151.62.127.88) (Ping timeout: 240 seconds)
2021-03-21 19:04:56 × wroathe quits (~wroathe@c-68-54-25-135.hsd1.mn.comcast.net) (Ping timeout: 240 seconds)
2021-03-21 19:05:18 × chenshen quits (~chenshen@2620:10d:c090:400::5:1038) (Quit: My MacBook Pro has gone to sleep. ZZZzzz…)
2021-03-21 19:05:32 <joel135> So it is a different symmetry than the one that spans have.
2021-03-21 19:08:21 × haskell_newbie quits (~haskellne@111.119.187.43) (Ping timeout: 264 seconds)
2021-03-21 19:08:48 rayyyy joins (~nanoz@gateway/tor-sasl/nanoz)
2021-03-21 19:09:01 <unyu> The opposite category would need to have a notion of exact sequence to begin with. This is certainly true in Ab, but I don't know it to be true in Grp as well.
2021-03-21 19:10:16 <unyu> Anyhow, I was intrigued by how I could have reached the stupid conclusion that “cographs are obviously uninteresting, because they are obviously isomorphic to the codomain”, when exactly the same (or rather, the dual) thing happens with the graph, and nobody calls the graph of a function uninteresting...
2021-03-21 19:10:52 × rayyyy quits (~nanoz@gateway/tor-sasl/nanoz) (Remote host closed the connection)
2021-03-21 19:10:53 ski . o O ( <https://en.wikipedia.org/wiki/Semidirect_product>,<https://en.wikipedia.org/wiki/Wreath_product> ; semi-direct products in monoidal parsing <https://www.youtube.com/watch?v=Txf7swrcLYs#t=28m58s>,<https://www.youtube.com/watch?v=HGi5AxmQUwU#t=41m15s> )
2021-03-21 19:11:18 rayyyy joins (~nanoz@gateway/tor-sasl/nanoz)
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2021-03-21 19:12:10 <ski> joel135 : would assume a zero object
2021-03-21 19:12:56 <joel135> Oh that's right.
2021-03-21 19:13:33 × royal_screwup21 quits (52254809@gateway/web/cgi-irc/kiwiirc.com/ip.82.37.72.9) (Quit: Connection closed)
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2021-03-21 19:13:54 <unyu> Who would have thought that semidirect products are useful for parsing.
2021-03-21 19:14:13 <Franciman> LOL
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2021-03-21 19:16:50 × heatsink quits (~heatsink@2600:1700:bef1:5e10:7956:c631:2eb4:a488) (Ping timeout: 264 seconds)
2021-03-21 19:20:22 <joel135> unyu: The distinction between graphs and cographs corresponds to the distinction between the two different factorizations of a morphism a -> b in a Quillen model category. Indeed, one of the morphism factors is called "trivial", corresponding to your " uninteresting".
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2021-03-21 19:41:23 hackage forex2ledger 1.0.0.0 - Print Forex quotes in Ledger format https://hackage.haskell.org/package/forex2ledger-1.0.0.0 (gregorias)
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2021-03-21 20:01:59 <joel135> ski: now i get the idea of monoidal parsing i think. thanks for mentioning it 1000 times :p
2021-03-21 20:03:47 molehillish joins (~molehilli@2600:8800:8d06:1800:c1f2:e355:53f0:4ab8)
2021-03-21 20:03:52 joel135 . o O ( https://en.m.wikipedia.org/wiki/Carthago_delenda_est )
2021-03-21 20:03:53 hackage IPv6Addr 2.0.0 - Library to deal with IPv6 address text representations. https://hackage.haskell.org/package/IPv6Addr-2.0.0 (MichelBoucey)
2021-03-21 20:07:27 <ski> hehe, joel135 :)
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