A quick question about the definition of adjoint, category theory.

Question

I am pretty new to fundamental terms of the category theory.

My textbook says that adjoint is:

$\mathbb{B}(F(A), B) \cong \mathbb{A}(A, G(B))$ ... obeying certain rules (which I skip).

Do I understand correctly: it requires a bijection between two sets of morphisms?

Answer 1

Yes. For two functors to be adjoint we require a bijection between those two sets of morphisms which obey those "certain rules", for each $A\in \Bbb A$ and each $B\in \Bbb B$.