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Stream: learning: questions

Topic: this lemma is false, but why?

Matteo Capucci (he/him) (Jan 25 2021 at 13:33):

I 'proved' this lemma, but apparently it is not true since it contradicts another true thing.
Can someone spot the mistake?
Screenshot-from-2021-01-25-10-39-50.png

Matteo Capucci (he/him) (Jan 25 2021 at 13:35):

One obvious thing is that every appeareance of $L$ and $R$ in the proof should be substituted by $L^{op}$ and $R^{op}$. I don't understand if this invalidates the proof, though.

Mike Shulman (Jan 25 2021 at 13:39):

Shouldn't the formula be $\mathrm{Lan}_L F(a) = \int^{b\in C} F(b) \times D^{\rm op}(L(b),a)$?

Matteo Capucci (he/him) (Jan 25 2021 at 13:40):

There it is! :face_palm:

Matteo Capucci (he/him) (Jan 25 2021 at 13:41):

Thanks!!