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Nov. 18th, 2010 | 03:04 pm

I might also post this to stack exchange, but I promised more wankery, so here I go.

In category theory, we've been talking about how goddamn near everything is adjoints. Specifically, this is where a lot of the duality that we notice in logic comes from; disjunction and conjunction are left and right adjoints to something, and the same goes for existential/universal quantification, etc. I have a few questions about this.

First, presumably the box and diamond modalities follow the same pattern. Where does the lax modality come in to play? I'm guessing it's not isomorphic to diamond, so it can't also be the left adjoint to whatever box is right adjoint to...but at the same time, it seems like since everything is a left/right adjoint pair, this shouldn't really be an exception.

Second, I'm guessing that in linear logic, 'with' and...'or'? 'circleplus'? Whatever. You know what I'm talking about. Anyway, it seems like those are also a pair of dudes. Does the same hold for tensor and par? If not, why not/what do we need to do to make it hold (ie, to make par exist)? And if so, does that help explain what the hell par actually means?

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Good news, everyone!

Nov. 16th, 2010 | 10:21 pm

I made a new livejournal with a less pretentious name! Freshman year, back when "professorsparks" was an inside joke, it seemed like a great idea for a username for everything ever. But now that "professorsparks" is a goal rather than a joke, it just sounds sort of douchey. So here I am, with a brand new livejournal! 

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