I am confused about what things should be thought of as "right" and what things should be thought of as "left" in category theory. Ideally, I would like answer like "left-handedness is mapping out of, right handedness is mapping into" along with a list of key notions that are left and right.
I think the following confusion might also be related.Why is the adjoint functor theorem is stated as it is?
Let $C$ and $D$ be locally presentable categories. The functor $F: C \rightarrow D$ has a right adjoint if and only if $F$ preserves small colimits.
Why does one always state this in terms of $F$ having a right adjoint, instead of $F$ being a left adjoint?