Thursday, February 10, 2011

so consider the presheaf topos of the walking arrow category as a ringed topos, via the identity arrow of some nice commutative ring k, perhaps a field ... and consider the (alleged...) dimensional category of invertible modules in this ringed topos ...

??essentially just one object ?? ... ??endomorphism ring of that object ??? ... ??or something???? .... ????

??something about ... "upper triangular matrix together with lower triangular matrix ... " ???maybe somethng about them being mates of each other or something??? hmm, but that doesn't constrain things too much ... ??? ...

?????....

hmmm....

?? ... "pointwise" tensor product ...

??so what _is_ the unit module here ??? ??maybe i mean as a module of 2X2 triangular matrixes?? ???or something ???? ...???....

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