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Monthly Archives: June 2006
Radical lax monoidal functors
In my previous entry, I deferred the problem of defining lax monoidal functors between radical monoidal categories. But yesterday evening on the train I realised that there is a cute way to think about lax monoidal functors, which makes it … Continue reading
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Rethinking monoidal categories
As you can probably tell, I’m hugely excited about Joachim Kock’s paper. I apologize to those of you who read it a year ago, and think I’m a bit late to the party. Most latestage PhD students, I imagine, have … Continue reading
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Kock on units
This morning’s crop of arxiv updates included a new version of Joachim Kock’s Elementary remarks on units in monoidal categories. Somehow I hadn’t noticed the earlier version; it’s a beautiful result, and it implies the lemma of mine that I … Continue reading
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Paré’s observation
It’s a curious (though well known) phenomenon that an equivalence in a bicategory can always be converted into an adjoint equivalence by tweaking one of the 2cells. There are two ways to prove it, that I know of. The elementary … Continue reading
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Fun with Rel
One of the great joys of category theory is the way you can so often watch familiar structures emerge unexpectedly from general constructions. It’s particularly amusing to apply the formal theory of monads to the 2category Rel of sets and … Continue reading
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On posetvalued sets
On Monday afternoon I had a look at Andrea Schalk and Valeria de Paiva’s paper on Posetvalued sets, which I was reminded of recently by Greg Restall’s survey of relevant and substructural logics. It gives a recipe for constructing models … Continue reading
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Monoidal centres
I was chatting to Craig “Cap. Astro” Pastro yesterday evening over a beer, and he mentioned an interesting question: if you take the monoidal centre of a braided monoidal category, do you get back the thing you started with? We … Continue reading
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