3 ms·
This is incorrect. The number of morphisms is not what makes mathematical objects more or less structured. What is correct is that the category of sets does not
by climatologist 3y ago
This is incorrect. The number of morphisms is not what makes mathematical objects more or less structured. What is correct is that the category of sets does not have constraints for morphisms between its objects. Bartosz is equating morphisms and "structure" which is not how most mathematicians think of what it means for a category or an object to be structured.
- klysm 3y agoIt seems incorrect to state that his perspective is categorically incorrect. The term “structure” lacks a precise definition and his interpretation isn’t completely invalid.
- js8 3y agoHe prefaces the statement with "my intuition tells me", so perhaps he is much less categorical (pun intended) about the claim than you interpret it.
- bmacho 3y agoIt is correct, in the best possible way. Having least structure is a soft/aesthetical statement, and the explanation is right after it (a correct definition). I wish all the math looked like this, first a soft/aesthetical statement, then right after the correct math.