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My evidence for this is that for = fibrations of univalent categories, cleavings are always canonical; on the = other hand, there is no foundational tweak that could make vector spaces ha= ve canonical bases. Best, Jon On Thu, Feb 1, 2024, at 11:06 AM, Thomas Streicher wrote: > Dear Jon, > > for constructing the opposite of a fibration you do not need at all > that the chosen cleavage is split. It is easy to see that fixing the > cartesian arrow also fixes the vertical arrow. > > If everybody is happy with this solution I am fine. It is in the same spi= rit > as chosen pullbacks or chosen finite limits. > The reason for my reluctance is that nobody would consider as a > natural notion a vector space with a chosen basis. > The virtue of strong choice is that then such additional structure can be > pulled out of the hat at demand. > > > Thomas ---------- You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. 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