I plan giving a homework problem on linear algebra for my students and my idea was to collect many results of diagram chasing.
Could you help me and give me some results of diagram chasing you know? They can be very basic or they can be more difficult. I think of results such as the "Five lemma".
PS: So far, they know all the basic stuff of linear algebra (vector space, linear maps, kernels, images, etc.). They don't know what is a finite-dimension space but they know what is a free/spanning finite families and finite basis.
PPS: They don’t know what is the quotient $E/F$... but maybe this can be overpassed by using subspaces $G$ such that $E = F \oplus G$.