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Category Archives: category theory
Revisiting “On editing text”
This document is an incomplete draft. About two years ago I wrote about a categorytheoretic treatment of collaborative text editing. That post is unique in the history of Bosker Blog in having been cited – twice so far that I know … Continue reading
Posted in algorithms, category theory, Mathematics
3 Comments
On editing text
Editing text is the opposite of handling exceptions; or, to put it another way, editing text is like exception handling but backwards in time. I realise this is an unexpected claim, so I hope you will permit me to explain. … Continue reading
Posted in algorithms, category theory
17 Comments
Games II
Last time, I explained how the category of finite simple games is equivalent to the initial liftproduct category. Now I want to show how this fact can be used to find nice ways of representing strategies.
Games I
When I started doing research, I mostly worked on categories of games. I even went so far as to write a firstyear report that suggested — even confidently claimed — that I would write a thesis on the subject. Well, … Continue reading
Posted in category theory, chatter
1 Comment
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
Posted in category theory, chatter
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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
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
Posted in category theory, chatter
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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
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 2category Rel of sets and … Continue reading
Posted in category theory, chatter
8 Comments
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
Posted in category theory, chatter
5 Comments