?? how filtered colimit (?? maybe just colimit of sequence ??) "gets promoted" to retract ??? ..... ???? colimit of sequence where all the arrows are the same idempotent ... ????? .....

"derived" / "higher" "stable" (??????) colimits .... ????? and relationship between filtered colimit and stable colimit ... ???? ....

?? extremal eckmann-hilton ... frankenstein ... ??? ... morita / karoubi .... ???? ....

?? .... ??? situation where .... shortage of "affine" stuff .... or existence of non-affine stuff, glued together from affine ... ??? but then progression (?? or degeneration ??? ... ????) to situation where after all everything qualifies as affine .... ????? what's happening in such situation ???? ..... ???? more objects ... ??? .... more morphisms ... ????? ..... ???? .... ???? ....

??? x^4 = x^2 example .... ???? try to work out .... ???? (and / or maybe x^3 = x^1) .... ????? .....

filtered colimits becoming retracts ... more retracts ... ???? .....