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Ban is not counital#258

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Ban-not-counital
Open

Ban is not counital#258
ScriptRaccoon wants to merge 2 commits into
mainfrom
Ban-not-counital

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@ScriptRaccoon

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This adds the easy proof that Ban is not counital.

It resolves #257.

@dschepler

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Looks good to me.

On a related note, I'm pretty convinced that the regular epimorphisms in Ban are exactly the linear contractions which are surjective on open unit balls - or equivalently, surjective maps $f : X \to Y$ such that the norm on $Y$ is equal to $\inf { |x| \mid f(x) = y }$. Which should make it pretty easy to show that regular epimorphisms are stable under pullback, and therefore Ban is regular.

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Is this a correct proof that Ban is counital?

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