Re: Fibrewise opposite fibration

[Nath Rao <khazanarao@gmail.com>]

[This no longer about how to define fibrewise opposite fibration, so may
be it is time t change the subject line.]

IMHO, this seems to be more like a religious war. In "mathematics in the
small", local axiom of choice allows us to choose representatives only
when needed. So we are grew up believing that putting things in the
definition that are not preserved by morphisms is "not done" (the
religious dogma) . But them we run up against issues when we try to do
the same thing in "mathematics in the large", and either ignore the
problem or argue endlessly about how to solve it.

Also, if are willing to assume that every set comes with a
well-ordering, why not assume a global well-ordering and be done with
it? [If I am going to use universes anyway, it seems to be trivial to do
this, as long as I live inside a fixed universe in any given proof.] For
ZFC, global choice is a conservative extension. Not being a logician, am
not sure, but perhaps it can be shown for global choice is a
conservative extension of local choice of 'all suitable set theories'.
Then we can do global choice with no qualms.

Regards
Nath Rao





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