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.

3 thoughts on “Category Theory I, the end in sight!”

  1. A tiny typo I’ve noticed: on page 75, line 18, the text reads “We saw. for example”, with a full stop instead of a comma.
    And I think on page 91 it’s supposed to be “its mirror image (Y×X, π2, π1)”, not “(X×Y, π2, π1)”?

    1. Thanks for the first — even the tiniest corrections appreciated!

      P. 91 is in fact correct as it stands. Maybe the use of “mirror image” is unhelpful. Look back at the original definition, if (O, \pi_1\colon O \to X, \pi_2\colon O \to Y) is a product of X with Y, then you’ll see that (O, \pi_2\colon O \to Y, \pi_1\colon O \to X) counts as a product of Y with X. Just apply that to the present case where we write X \times Y for O. (Maybe I should spell this out better!)

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