# 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

## 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 late-stage PhD students, I imagine, have … Continue reading

Posted in category theory, chatter | 8 Comments

## 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

## 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 2-cells. There are two ways to prove it, that I know of. The elementary … Continue reading

Posted in category theory, chatter | 8 Comments

## 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 2-category Rel of sets and … Continue reading

Posted in category theory, chatter | 8 Comments

## On poset-valued sets

On Monday afternoon I had a look at Andrea Schalk and Valeria de Paiva’s paper on Poset-valued 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

Posted in category theory, chatter | 5 Comments

## 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

Posted in category theory, chatter | 1 Comment

## More on strictification

Another fascinating day! At lunch time Steve Lack told me some interesting things about the strictification operator for bicategories. Apparently section 5.6 of [GPS] is wrong, and Steve reckons Gray is probably not triequivalent to Bicat. (The mistake in 5.6 … Continue reading