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My evidence for this is that fo= r fibrations of univalent categories, cleavings are always canonical; on th= e other hand, there is no foundational tweak that could make vector spaces = have canonical bases. I agree that from a univalent point of view all cleavages are equal. But from a univalent point of view all cleavages are even split! That is a bit too much for me (see Warning (1) on p.10 of my notes on fibered cats). But I do not want to take up old discussions! I really prefer to disagree. Instead I admit that all choices of cleavages are uniquely isomorphic which certainly is not teh case for bases. Thomas ---------- You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as= hx?source=3DEscalatedMessage&action=3Dleave&GuestId=3D4eb9b40c-9b3a-48a5-97= 81-836e5a171e8b