# Category Archives: category theory

## Revisiting “On editing text”

This document is an incomplete draft. About two years ago I wrote about a category-theoretic 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 lift-product category. Now I want to show how this fact can be used to find nice ways of representing strategies.

Posted in category theory, chatter | Tagged , | 1 Comment

## Games I

When I started doing research, I mostly worked on categories of games. I even went so far as to write a first-year report that suggested — even confidently claimed — that I would write a thesis on the subject. Well, … Continue reading

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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