?? moore-postnikov factorization for maps of chain complexes, vs some sort of "dual moore-postnikov factorization" for spaces ... ???.... ??? product structure ?? .... ???? ....

?? intersection homology of space with only 0-stratums singular .... ??? maybe some sort of "splicing" ??? .... ?? "moore-postnikov" ??? ..... ????? "lower half from upper stratums, upper half from 0-stratums" ??? ..... ??? .... ??? "mapping cone" .... ????? of map of spaces and/or of complexes ????? ... ??? ....

visualization of rank 2 real-algebraic buildings (length?)

?? might advocate position that representation theory of lie groups is secretly ess study of this geometry .... ???? ....

?? generalized pluecker relations .... ???

?? stratification of affine n-space by axises ..... ?? or "axis planes" or something .... ?? ... ?????? ..... baez-dolan .... woolf .... ??? .... ?? projective n-space .... ???? .... "configuration space" and braid group .... vs symmetric powers and thom-dold .... ???? ..... thom-thom ..... ????? .....

?? zero perversity ..... ???? .... confusion about ... ??? whether stuff here (...) is agreeing with idea that "adjoints all the way up automatically amounts to inverses" .... ??? .... "transversality as generic" ..... ????? .....

?? 0th intersection homology as something like measures on the space of highest stratums ?? .... just a fairly wild guess ... ??? ....

(?? hmm, but ... ?? non-dependence on stratification .... ???? .... ?? in "nice" case ?? .... ... ??? hmm, maybe it's actually ok ???? ...... ??? .... ???? cutting out an ordinary point as failing to break off new components ... ??? .....)

?? degeneration .... ???? .....

?? segal category .... ??? ....

?? thom spectrum ... ??? ....

??? hartog .... ????? ......

??? "intersection theory" (?? ...) for toric varieties .... ???? ....

?? intersection homology of cone ... ??? ....

?? zero perversity .... transversality .... baez-dolan .... woolf .... ???? .....

?? top perversity as non-vacuous ???? ...... ?? in what sense top, then ??? ....

?? 2 3-simplex 2-skeletons glued together at a 0-simplex ... ???? ....

?? so ... let's try checking whether top perversity is vacuous ... ???? ....

real-dimension("intersection(i-chain x,stratum m-k)") <= i - k + top-perversity(k)

?? top-perversity(k) = k-2 ???

i - k + top-perversity(k) = i - 2 ?????? ..... ???????? .......

?? domain of perversity starts at 2 .... ???? no constraint on how i-chain intersects the two highest stratums ???? ....

?? m = 2 .... ???

0-chains and 1-chains must completely avoid the 0 stratum ???? ...... ???? ...

?? ....

?? [doctrine vs 2-topos] vs [tendency to try to see (possibly higher) category of spaces as opposite of 2(??? ....)-category of theories (in form of .... ??? consisting of their syntactic categories and interpretations between them ... before taking opposite .... ??? ....) ... ( me ... ??) vs tendency to try to see it as topos (lawvere ... ?? grothendieck?? ...)]

?? lots of duality confusion here, among possibly other kinds ??? ... ?? level slips as to which sort of duality flips .... ???? .....

?? understanding torus-equivariant quasicoherent sheaves from accidental topos viewpoint .... ???? ...

?? relationship between "perverse sheaves as forming alternative core of infinity-category of complexes ..." and "intersection homology relative to a perversity, using sub-complex of chains allowable wrt the perversity ..." ??? ..... ????? ....

?? am i supposed to be thinking that the intersection homology of a stratified space is ... ?? more or less like the ordinary homology of smooth spaces that degenerate into it ?? .... ??? ....

?? or is ordinary homology already supposed to be "continuous wrt degeneration" ?? ...
?? poincare duality .... ???? ...

?? "variation of hodge structure" ??? .....

?? "flat" .... ???? .....

?? intersection homology of bunch of spheres with finite number of finite identifications .... ??? ....

?? "attachment" and "blowing up" ??? ..... ????? un/reliability of blowing up as means of "resolving singularity" ??? ..... ???? ...

?? drawing a bunch of points, and maybe some infinitesimal rays at each point .... then pairing them up with connecting paths .... ????what are all the things that this reminds me of ???? .....

??? spherical vs projective here ????? ..... ??????.....

?? intersection homology here .... ???? .....

?? vasilieff ... ????

?? "the locally cone-like structure of a topological pseudo-manifold" .... (p 53 ...) ??? "chart" / "glueing" approach to pseudomanifold ???? ...... ???? .....

?? maybe not really ... cone over arbitrarily complicated pseudomanifold, recursively ... ???? ....

?? r^2 X cone(-1d stratified space)

?? r^1 X cone(0d stratified space)

?? r^0 X cone(1d stratified space) ...... ????


??? cone on figure 8 ??? .....

proj geom= dimensional analysis 5 ?

interpretations of "tannakian" ... ????

"logic" .... "algebraic geometry as branch of logic" ..... ???? .....

"unification" ...

"correspondence between tensor cats and stacks" .... ???? ..... ??? "categorified (affine ...?? ...) alg geom" ???? .... ?? this last as maybe separate fourth interpretation ???? ......

?? try taking nice simple (but somewhat "interesting" ...) example of "toric line bundle" and see whether it has some nice obvious toric equivariance structure .... ???? ....

proj geom = dimensional analysis 4

0 throat-clearing ...

1 introduce example

2 ????? .... lawvere's category interpetation, somewhat contrasted against graded comm alg interpretation

3 ?? moduli stack ... ??? presumably coincidental similariy to "model" .... ??? badness of stack, maybe ??? .... ?????? ...... ????? ....

????? .....

?? to what extent does "_the_ degenerate model" of a dimensional theory exist ???? ..... ??? pointedness of certain 2-cat ?? .... ??? "holding grade zero constant" ??? ..... ????? .....