Note on the files below: When a chapter begins on an even-numbered page, the file below begins with a blank page, for convenience in 2-sided printing. So if you display a file and see a blank page, just page forward to see the text.
Currently (Jan. 2008) the Berkeley Math Department printers misbehave on PostScript files of the sort used here. However, these files can be printed successfully using the unix command sed "1s/-1.0//" filename | lpr .
The situation with the PDF files is, unfortunately, even more complicated. The versions given below seem to come out OK on our Department printers, though when viewed with Acrobat, or printed on some other printers, the character I have used to draw the horizontal bar of arrows (e.g., on p.21 in Chapter 2) is vertically displaced, so these arrows appear "broken". I can produce a version in which this is "corrected", so that on those platforms the arrows look right; but then they come out broken on our Department printers. The link "pdf_alt" under Chapter 7 below is an example; if you have a printer which gives broken arrows on the regular PDF files below, you might try that file on it.
Table of contents, together with
Chapter 0, About the course, and these notes, and
Chapter 1, Making some things precise.
ps pdf
Chapter 2, Free groups. ps pdf
Chapter 3, A Cook's tour of other universal constructions. ps pdf
Chapter 4, Ordered sets, induction, and the Axiom of Choice. ps pdf
Chapter 5, Lattices, closure operators, and Galois connections. ps pdf
Chapter 6, Categories and functors. ps pdf
Chapter 7, Universal constructions in category-theoretic terms. ps pdf alt_pdf
Chapter 8, Varieties of algebras. ps pdf
Chapter 9, Algebra and coalgebra objects in categories, and functors having adjoints. ps pdf
Answers to some students' questions in Math 245, Spring 2008 taught from the above text.