Re: [HoTT] Injective types

[Nils Anders Danielsson <nad@cse.gu.se>]

On 02/05/2019 22.46, escardo.martin@gmail.com wrote:
> I can confirm from a 26k line Agda development (with comments and
> repeated blank lines removed in this counting of the number of lines)
> that not once did I need to embed a universe into a larger universe,
> except when I wanted to state the theorem that any universe is a
> retract of any larger universe if one assumes the propositional
> resizing axiom (any proposition in a universe U has an equivalent copy
> in any universe V). So I would say that such situations are *extremely
> rare* in practice.

I once wrote some code where I made use of univalence at three different
levels. Does anyone know if one can prove that univalence at one level
implies univalence at lower levels, without making use of cumulativity?

-- 
/NAD

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