Re: RE : categories: Re: Not invariant but good

[Thomas Streicher <streicher@mathematik.tu-darmstadt.de>]

Thanks Andr'e for pointing out by various examples why it is not always wise
to insist on invariance under equivalence or weak equivalence. This in my
opinion is the real issue and not whether "evil" is a tasteless name or not.

The problem rather is that people using "evil" really mean it so even if they
deny it.

An little comment on structure versus property which is an importnat
distinction in my eyes. The notion of Grothendieck fibration is a property
of functors and not an additional structure. However, the notion of fibration
in a(n abstract) 2-category can be formulated only postulating a certain kind
of structure which, however, is unique up to canonical isomorphism. But this
amounts to defining Grothendieck fibrations in terms of cleavages (which
certainly are all canonically isomorphic). But choosing cleavages amounts
to accepting very strong choice principles which is maybe no real problem
but at least aesthetically moderately pleasing.

Thomas


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