Sunday, May 29, 2011

??recent insight into terminology "reflects" (with sort-of relationship to "reflective subcategory" ... ?? ...) as still leaving mystery of terminology "creates" .... ????.... ??don't see any relevant concept of "creative subcategory" (??? ...) offhand ... ???...

"preserve colimits" =?= preserve colimit cocones =?= preserve universal co-yoneda morphisms ... ???

???? universality of co-yoneda morphisms as appropriate concept (??for certain purposes ?? ...) even when only some co-yoneda niches are universally filled ?? ...

"reflect colimits" =?= preserve non-universal co-yoneda morphisms ???....

"create colimits" =?= ... ???... ????preserve non-universally-occupied-ness of co-yoneda niches ???? ..... ???? ....

??preserve failure of specific something to be universal niche-occupant, vs preserve failure of there being any universal niche-occupant ... ???...

"preserve failure" and "create" ... ??? "superman" phenomenon here ??? ???... ??downstairs universal niche-recipient ... ????... as superman candidate for image of upstairs universal niche-recipient .... ????? ..... ??at least narrows down filed of upstairs candidates to some extent ???.... ??? .... in "superman" way .... ??? meaning that maybe there isn't actually any satisfactorily qualified candidate... ??? .... ... not sure i've got this quite straight here yet ...

????"reflection" onto _non_-full subcategory ???? .... ???should at least sort of exist, though maybe somehow not really important for certain present purposes ??? ??"correlation between moore-postnikov-like factorizations of adjoints" ... ?? seems like might become more complicated (?? ...) in "higher-dimensional" case ... as usual i guess ... ???....

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