>>16734712
a. f,h are two-to-one (except at 0) but f is injective
b. if f=ag and g=bh then f=abh
c. f=f(id)
d. one direction takef^(-1) where defined, id everyehere else. other direction if f is not 1:1 then no hf is gonna be 1:1
e. g=gf
f. prev part one dorection, other direction is because if f is constant then hf is constant for all h
g. (d) inj forms a class (c) its the top one (f) const form a class (e) its the bottom one