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.
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)”?
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
is a product of 
with 
, then you’ll see that 
counts as a product of 
with 
. Just apply that to the present case where we write 
for 
. (Maybe I should spell this out better!)
Whoops, that makes sense. Thank you!