?? “formula object which believes given cocone is universal” …. ??? vs model which “believes” it …. ??? …. ???? …..  ??? “morphism st its target believes it to be an isomorphism” …. ???? …..

??? other (??? ……) formula / model confusion near here …. ???? …..

?? can we just “take some graded module that we know is supposed to be corrected to something else but st that correction isn’t forced by the axioms that we have so far, and make a new axiom out of it …” … ?? simply by saying that that morphism should be invertibilized ?? …. ???? …

“conservative” as complementary to “does nothing but invert morphisms …” … ??? analogs of this … ?? “does nothing but universally promote certain cocones to universal” … ???? …. ??? ….

??? “reflect …” … ??? pun ?? … ??? ….

?? notes from discussions with brandenburg …. ???? ….

??  toric universe of semilattices ??? …. ….