# Talk:Introduction to Category Theory/Sets and Functions

Latest comment: 6 years ago by Olivierd in topic Inverse

You should definitely take a look at Lawvere's Sets for Mathematics for a fantastic presentation of the category of Sets from a categorical perspective. -- Marc (The preceding unsigned comment was added by 74.139.215.32 (talkcontribs) 22:14, 9 November 2007)

I've seen Lawvere's book but can't recommend it to beginners. It's a non-standard approach and imho foundational issues don't belong to an intro course. It's a good first book for 'logic-branch' of category theory. Tlep 10:00, 10 November 2007 (UTC)

Can anyone check if the n^2 - 4 set is what it claims to be?

Wouldn't it make sense to state and prove that an injective function has a left inverse, for symmetry with the discussion of surjective functions? And shouldn't one discuss what an inverse is before bringing up that either of these have inverses?

Sorry for the stupid questions but shouldn't idX in the first part of proof of Proposition related to Injection be idY? --Oct09

 I noticed it as well and fixed it. -- Oct10


## Inverse

I have doubts about the paragraph that starts with "Injective functions with non-empty domain have left-inverse".

If we have injection ${\displaystyle f:X\to Y}$ , then the inverse ${\displaystyle g}$  is not (generally) defined on all of ${\displaystyle Y}$ , but only on the range of ${\displaystyle f}$ .

## Partial Functions

In the introduction to functions it is stated that for every element x in X there is a y for which y = f(x). In effect this forbids partial functions. This condition is then forgotten in the proof that injections imply left-inverses. The left-inverse may be partial and hence fail this definition of function.