2026/06/29

2026-06-29 00:07:09 +0000 <monochrom> Err, Two is the diagonal functor itself heh.
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2026-06-29 00:33:03 +0000finsternis(~X@23.226.237.192) finsternis
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2026-06-29 00:58:08 +0000vgtw(~vgtw@user/vgtw) vgtw
2026-06-29 01:06:25 +0000czan(~czan@user/mange) czan
2026-06-29 01:06:52 +0000tzh(~tzh@c-76-115-131-146.hsd1.or.comcast.net) (Quit: dnvln)
2026-06-29 01:12:56 +0000 <schuelermine> so is the adjoint Two ⊢ Id?
2026-06-29 01:17:56 +0000Everything(~Everythin@static.208.206.21.65.clients.your-server.de) (Remote host closed the connection)
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2026-06-29 01:48:55 +0000ft(~ft@p3e9bcc42.dip0.t-ipconnect.de) ft
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2026-06-29 02:35:58 +0000 <monochrom> I think no. I forgot what I used.
2026-06-29 02:37:51 +0000schuelermine(~Thunderbi@user/schuelermine) (Ping timeout: 252 seconds)
2026-06-29 02:39:30 +0000ft(~ft@p3e9bcc42.dip0.t-ipconnect.de) (Ping timeout: 252 seconds)
2026-06-29 02:41:26 +0000ft(~ft@p3e9bcfda.dip0.t-ipconnect.de) ft
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2026-06-29 02:47:19 +0000ft(~ft@p508dbc65.dip0.t-ipconnect.de) ft
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2026-06-29 02:53:36 +0000ft(~ft@p4fc2ac9e.dip0.t-ipconnect.de) ft
2026-06-29 02:58:11 +0000 <dolio> There is a functor Δ : C → C × C that will take an object A to (A, A). A right adjoint would be G : C × C → C with (A, A) → (X, Y ≅ (A → G X Y). This is a product functor for C if it exists. Two is the monad of this adjunction. η comes from the identity on ΔA transposing to A → Two A...
2026-06-29 02:59:22 +0000 <dolio> If you look at the identity X×Y → X×Y, this transposes to Δ(X×Y) → (X, Y). These will be the first and second projections of X×Y. μ for the monad arises from this.
2026-06-29 02:59:30 +0000ft(~ft@p4fc2ac9e.dip0.t-ipconnect.de) (Ping timeout: 248 seconds)
2026-06-29 02:59:59 +0000tzh(~tzh@c-76-115-131-146.hsd1.or.comcast.net) tzh
2026-06-29 03:01:21 +0000ft(~ft@p3e9bc5ec.dip0.t-ipconnect.de) ft
2026-06-29 03:03:54 +0000 <dolio> It's going to run π₁ on the first row and π₂ on second row.
2026-06-29 03:14:38 +0000bikeshed(~bikeshed@user/kidcoconut) kidcoconut
2026-06-29 03:21:04 +0000bikeshed(~bikeshed@user/kidcoconut) (Quit: 23)
2026-06-29 03:26:19 +0000user363627(~user@user/user363627) (Quit: Konversation terminated!)
2026-06-29 03:26:39 +0000user363627(~user@user/user363627) user363627