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 01:12:56 +0000 <schuelermine> so is the adjoint Two ⊢ Id?
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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)
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2026-06-29 02:41:26 +0000ft(~ft@p3e9bcfda.dip0.t-ipconnect.de) ft
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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.
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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
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2026-06-29 03:26:39 +0000user363627(~user@user/user363627) user363627
2026-06-29 03:39:57 +0000 <monochrom> Ah right, thanks.
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