Tuesday, January 17, 2012

?? cartesianness ...... ????? ....

?? as property vs as structure .... ???

?? as something that can be (??2-)predicated of a monoidal abstract category in a cartesian monoidal 2-category only because a monoidal abstract category in a cartesian monoidal 2-category is automatically a co-stable bimonoidal abstract category in the underlying stable monoidal 2-category .... ???? ....

?? contractible ..... ???? .... bit about ... "no interesting span-maps between map-spans" (??? ... ??? ....) .... ??? as maybe related to ... certain paradox / confusion about "contractableness" ... "killing homotopy groups" ... ?? "why isn't everything always boring?" .... ???? hurewicz(??...)'s mistake ...

?? crackpot .... ???? .....

?? matrix .... ???

?? relationships among various variants on "matrix" ....

?? matrix with coefficients in given rig / ring ...

?? operation in prop for certain kind(s ...) of bimonoid .... ?? how did that bit go ??? spans with extra total order structure on certain fibers .... ???? ..... idea that didn't quite seem to work .... ????? .....

?? braid ... ??? ...

?? microcosm .... ??? .... ??? hopf .... ???? .... cartesian .... ???? hopf monoid vs mere bimonoid ... ???? .....

?? kennen vs wissen and ... ??somewhere in moore-postnikoff hierarchy ... ??? ....

??? left-universal property of n-cat given by set,span,span, ... ,span,span,map ?? ..... ????? ...... ???? ....

?? some stuff jeff mentioned ... ?? various "reductions" of span concept ... level slip .... ???? ... ??? .....

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