??so what about "karoubi envelope of an operad" ??? ... or something ...

??suppose we have a morita equivalence (??of operads?? ... or something ??...) e : x -> y ... ??and also a morphism m : y -> z .... ???then ... ??is there a nice concept here of... ??"the x-analog of z" ??? or something?? ....

hmmm ... ???some sort of "distributivity between morita equivalences and morphisms" ?????? or something ???? .....

???what about something about ... ???expressing a morita equivalence as a span of morphisms .... ????or something??? .... ???span of "morita morphisms" ??? ...

a,b : x <- s -> y span of morita morphisms ... ????....

??what about "weak pushout of bm along a" ... ???or something ...

??maybe for operads the morita span apex should be allowed to be a prop ??? ... ??or something ???.... ??or maybe not necessary??? ??? or something ???...

??so... ???karoubi envelope of typed k-linear operad .... ???...