among other things, i'd like students to come away understanding the following.
(1) the fundamental groupoid and the equivalence $Cov_X \simeq Fun(\Pi_1(X),Set)$ of categories, for a nice topological space $X$.
(2) the following articulation of eilenberg--steenrod:
(a) the $\infty$-category of finite spaces is freely generated by the point under finite colimits.
(b) the derived $\infty$-category of a ring is stable.
(c) optional: (i) the $\infty$-category of spaces is freely generated by the point under colimits. in particular, finite + filtered = all. (ii) the derived $\infty$-category of …