/sci/ - Science & Math

>>11071772
What do you refer to with the "class" an brackets?

Do you just mean they form a class as in
>>11071768
?
I'd reason the fact that a group theory in ZF foundations is defined as a set with a binary operation is pretty much another set theory artifact.
Classes are just as good collections as sets (or do you really need to put your collection of group elements inside another set to study your group for some reason?)
Being the goto example of universal algebra, you don't even need an existential quantifier to speak about groups, pic related.
Reasoning another way, you just need product (pullback over a terminal object) and three arrows
m : G × G G, e : 1 G, inv: G G
for a group object. Don't need for G to be a set for anything, I'd say