Timeline for Set theory for category theory beginners
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2010 at 3:40 | comment | added | The Mathemagician | Lawvere and Rosebrugh IS excellent and of course,Lawvere has long been one of the most active and vocal advocates of the creation of a unified foundation for both set theory and category theory. The book is written very much with this ultimate goal in mind.My problem with the author's approach is they practically eliminate membership and equality then becomes synonomous with isomorphism. I have a HUGE problem with this-without some stronger concept of equality,all kinds of wacko things start to happen in mathematics.See the thread dealing with equality vrs.isomorphism. | |
| Nov 24, 2009 at 13:34 | comment | added | Tom Leinster | You're right; I overstated my case. When you look at the book, it doesn't immediately give the impression of "how mathematicians think about sets". What I wanted to say is that their axiomatization of set theory (using sets and functions) consists of a list of statements that correspond to features of sets as used by ordinary mathematicians every day. The same is not true of ZFC (which axiomatizes sets and membership). For instance, ZFC's Axiom of Foundation implies that there is some real number none of whose elements are real numbers. To most people, that statement is nonsensical. | |
| Nov 23, 2009 at 22:03 | comment | added | John D. Cook | Thanks for pointing out my ommision regard Rosebrugh. I added his name. Perhaps the book shows how algebraists think about sets, but it's far from how I (as an analyst) think about them. I came to the book already knowing set theory and wanting to learn a little category theory. I thought that's how most people would approach the book, but I suppose some folks might learn in the opposite order. | |
| Nov 23, 2009 at 21:57 | history | edited | John D. Cook | CC BY-SA 2.5 |
added 14 characters in body
|
| Nov 23, 2009 at 21:39 | comment | added | Tom Leinster | For the record, it's by Lawvere and Rosebrugh, not Lawvere alone. Also, I think the name is spot-on. It's an approach to set theory that's very closely tied to how most mathematicians use sets in their daily practice (unlike the traditional approach). | |
| Nov 23, 2009 at 18:15 | history | answered | John D. Cook | CC BY-SA 2.5 |