Peter Smith's Blog, page 19

Category Theory I — one last revised draft

I didn’t intend to put another version of Category Theory I online before the positively final version for paperback printing was available. But I’m going to be caught up with other things including a short family holiday for a few days, so I am after all going to post this almost-final version now. What’s left to do? Finish the index of notation, design a cover, get things into the Amazon print-on-demand system. The paperback should be out by about August 10.

I’ve corrected some typos. But the main changes are that I have deleted  §16.7 on ‘naming’ arrows, and the whole of what was the short but dense Chapter 24 on power objects. Both seemed in retrospect a bit out of place in what is billed as ‘Notes towards a gentle introduction’. The material in §16.7 wasn’t mentioned again (I hope!); and the details in Chapter 24 also go far beyond what is really needed at this stage.

The latest version of Category Theory I, with Category Theory II updated to keep theorem numbering etc., can be downloaded here.

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Of making many intro logic books there is no end

There was an interesting post on Daily Nous by Curtis Franks a few days ago. He starts with some comments on the much used book and software package Language, Proof and Logic (LPL) by Jon Barwise, John Etchemendy, and Dave Barker-Plummer. I do agree, by the way, with the criticisms. Franks’s discussion then opens out to look at some other intro logic texts, with and without associated courseware.

There are a number of books mentioned that are not familiar to me, but then I haven’t been keeping up with what’s out there. I’ll have to dip into those that are available online sometime. Curtis Franks doesn’t mention Nick Smith’s excellent text at all (rather a surprise), so I’m in good company, as he doesn’t list my IFL either. One commentator mentions using IFL but his students finding it too challenging as soon as it moves beyond the initial very introductory chapters (that soon?)

It is sheer madness I know, but despite the multitude of intro logic texts, I confess I am still inclined to have another bash at an entry-level book, Another Introduction to Formal Logic. But freed from the IFL1 constraints of fitting round the then first-year Cambridge syllabus, or the IFL2 constraints of length and level for the CUP Introductions to Philosophy series, I’d structure it rather differently and make it slightly more sophisticated, and indulge myself …  There is no point in trying, impossibly, to please everyone!

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Leonkoro Quartet and Elisabeth Brauss

Just a note of a BBC broadcast of a concert from the Cheltenham Festival, with the terrific multi-prize-winning young Leonkoro Quartet and the equally terrific Elizabeth Brauss. They played Webern’s Slow Movement for String Quartet, Schulhoff’s 5 Pieces for String Quartet, and then Schumann’s Piano Quintet in E flat major, Op 44.

Wonderful, I thought.

A link to the concert on the BBC website.

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Category Theory I, a complete draft

So, at long last, a full draft of Category Theory I is online.

There are now thirteen added pages of content, plus an index of definitions. The main substantive change is the added last chapter on ‘the elementary theory of the category of sets’.

I’ll draw breath, do a quick-ish end-to-end read for consistency, and aim to get a print-on-demand paperback set up by the end of the month. That won’t be to fix the text once and for all: I’m thinking of this as a beta version, and an easily revisable paperback will just be there for those (including me!) who find a 228 page printed book easier to work from and comment on than an onscreen PDF.

Of course (and you know what’s coming next, because I’ve said it before), if you have been meaning to drop me a note with comments/suggestions/corrections, then now — yes, really now — is the time to do so!

Current versions of Category Theory I and II can be downloaded here.

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Just a distraction

Not for the first time in my life, I went to the Apple Store, saw, was tempted, fell …

So I’m writing this on a spanking new 15″ MacBook Air. With a pretty good trade-in price for my not-so-old 13″ MBA, an education discount, and a generous Fathers Day gift-token, it wasn’t too outrageously self-indulgent. And I’m loving it, seems perfect for its intended role as a stay-at-home, but move-from-room-to-room, work machine. The additional screen real-estate is definitely worth having e.g. for LaTeX.

Setting this up has been a distraction from matters categorial. Yes, of course I know you can get a new Apple machine to painlessly and very quickly clone your old one. But I accumulate a lot of rubbish in three years (never used trial apps, never-read downloads, etc. etc.) — don’t we all?  So I find that it is in the end worth the time and effort to do a spring clean when I get a new machine. What nerdy fun …

(For those who might care about these things, I got the base model again, as I have not once had memory problems with the base model M1 MBA; the memory pressure indicator stays steadily green for me. And after a couple of Space Grey MacBooks, I’ve reverted to the classic Silver. It’s classic for a reason, as the Daughter remarked … And one look at the condition of the Midnight machine in the store  was enough to tell me that the fingerprints issue would drive me spare.)

Actually, that’s not the only thing that has just got in the way of finishing Category Theory I. I’ve decided to say just a bit more about toposes and about ETCS that originally planned, and I’m just needing to think through how to arrange things. Nerdy fun of a different kind.

Though hours have just disappeared because a search (just prompted by a prior search) revealed that I’d used the word “just” just about ridiculously often. Seven times on one page was the record. Easy enough to go through, rephrasing, deleting, replacing with ‘only’, ‘simply’, ‘merely’, as seemed best. But bang goes most of an afternoon …

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Category Theory I, the end in sight!

A further revised version of Category Theory I is now online. The main substantive changes are in the last few chapters. In particular, the short Chapter 24 on power objects is much improved.

There are also quite a few corrections of typos and thinkos — I should particularly thank Ruiting Jiang of the Queen’s College Oxford for comments.

What’s left to do before I paperback these notes? Add a final chapter on ‘the elementary theory of the category of sets’ as all the pieces are in place to cover that and an add an index. So to repeat what I said a couple of weeks ago, but with a tad more urgency, if you have been meaning to drop me a note with comments/suggestions/corrections, then now — yes, really now — is the time to do so!

Current versions of Category Theory I and II can be downloaded here.

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The Pavel Haas Quartet at Wigmore Hall

The great PHQ played a short concert of music by Czech-born composers at lunchtime today at Wigmore Hall. The medieval chorale on which the Meditation by Dvořák’s pupil and son-in-law Josef Suk is based is still well known in the Czech Republic. Martinů’s Second Quartet (1925) was the first of his works to garner him international attention. Brno-born Korngold’s Third Quartet dates from 1944-5.

This was one of PHQ’s first concerts with their new permanent (oh, let’s hope!) viola player. They have had troubled times in that position since their founder violist Pavel Nikl sadly had to leave the quartet in 2016 due to family illness, and have taken their time after another sudden departure to settle on a replacement. They have played a number of concerts to much acclaim with the terrific Dana Zemtsov (who is based in Amsterdam); but it is very understandable — famously intensive rehearsers that they are — that they have in the end chosen to work from now with another Slovak living the Prague, another fine player, the young Šimon Truszka, previously of the Kukal Quartet. May it work out well for all of them! We need PHQ to be back in the recording studio.

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Day 471

It has been a beautiful early summer’s day here in Cambridge. Our small garden — ok, let’s be honest, it’s entirely Mrs Logic Matters’ garden — is looking lovely. There’s a wild profusion, foxgloves, clematis, geraniums, roses, irises, the last forget-me-nots, another patch of blue where the ceanothus is flowering, daisies on the grass path. The other side of the lane at the bottom of the garden, there is beautiful wall of tall trees so we are surrounded by green, remarkably so for a city house. A jay has just flashed by; one of the local squirrels (annoying but cute) is posing on the fence; our blackbird with his so-recognizable-phrases has been singing his heart out in between his almost daily territorial skirmishes with a neighbour who has distinctive white feathers. An early evening glass of Gavi waits on the little table outside, while a robin snatches supper a few feet away. Despite the proximity of the inner ring road, it is now very quiet. Peaceful, even.

In Ukraine, it is Day 471 of the war.

This is not how I expected things would be, waking up each morning to read of war in Europe. A vicious ground war, targeting civilians in barbaric ways. Cities and towns devastated, hundreds of thousands displaced, children abducted, prisoners tortured, God knows how many killed and maimed. And now a vast area flooded by blowing up a damn. Sitting in peace in an English garden, it is almost impossible to get one’s head around the fact that this is all happening, here and now. But on and on it goes.

In Ukraine, it is Day 471 of the war.

It resets one’s thinking about so much. Yes, things here are are in miserable slow decline. The physical manifestations hit your eye everywhere, even in a comparatively rich city like Cambridge. The boarded shops, even in the very centre; other nice stores being replaced by cheap rubbish;  creeping shabbiness; roads not mended … oh you know the kind of thing. Below the surface too, things work less and less well; elderly friends swap experiences of an NHS hardly coping; a referral to the “rapid chest pain clinic” may result in an appointment in six weeks if you are lucky … And so it goes. The poor are getting poorer. And I won’t start on the political situation,  But reset! Let’s put things in perspective. Ye gods, in the wider scheme of things, all that — if very far indeed from being trivial or unimportant — is still not exactly terrible.

But in Ukraine, it is Day 471 of the war.

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Category theory Notes updated again (and again)

A revised version of Category Theory I is now online. The main substantive change is a rather more consistent handling of plural notation; but there are a couple more theorems and some scattered improvements in explanations and a few typos corrected.

There is a corresponding new version of Category Theory II but the only changes are ones to automatically update cross references to Category Theory I.

I plan over June to turn Category Theory I into a very cheap paperbacked Big Red Logic book (though it will of course still be free to download as a PDF). The text still won’t be set in stone — in fact, I’ll call it a β-version. But it will be a lot nicer to work from.

I plan to add one more chapter, on ‘the elementary theory of the category of sets’ as all the pieces are in place to cover that. I have a fairly short current list of previous episodes I want to improve, though I will no doubt find more; I want to add more signalling about which more techie bits can be skipped by those wanting a less proof-heavy (initial) read; I’ll add an index. So if you have been meaning to drop me a note with comments/suggestions/corrections now is the time to do so!

Current versions of Category Theory I and II can be downloaded here.

Added June 6: Minor revisions and typo-corrections for  Chapters 1 to 6 uploaded.

The post Category theory Notes updated again (and again) appeared first on Logic Matters.

Category theory Notes updated again

A revised version of Category Theory I is now online. The main substantive change is a rather more consistent handling of plural notation; but there are a couple more theorems and some scattered improvements in explanations and a few typos corrected.

There is a corresponding new version of Category Theory II but the only changes are ones to automatically update cross references to Category Theory I.

I plan over June to turn Category Theory I into a very cheap paperbacked Big Red Logic book (though it will of course still be free to download as a PDF). The text still won’t be set in stone — in fact, I’ll call it a β-version. But it will be a lot nicer to work from.

I have a fairly short current list of episodes I want to improve, though I will no doubt find more; I want to add more signalling about which more techie bits can be skipped by those wanting a less proof-heavy (initial) read; I’ll add an index. So if you have been meaning to drop me a note with comments/suggestions/corrections now is the time to do so!

Current versions of Category Theory I and II can be downloaded here.

The post Category theory Notes updated again appeared first on Logic Matters.