All Questions

In material set theories (like ZFC), one can prove that there is no set of all sets. Can one prove a similar statement in ETCS? This exact statement "there is no set x such that y in x for every set y"...

There's a quantifier ("binder", whatever), call it $\alpha$, defined as follows: $\alpha x.\tau$ is the (usually infinite) expression obtained by applying the substitution $\{x \mapsto \tau\}$ to the ...

Please forgive me if this question sounds too naive... Well, in mathematics a formal theory consists of a collection of axioms $T$ (such as Peano arithmetics, or Group Theory, or ZFC), which ...