  We give a new definition, simpler but equivalent, of the abelian category of
Banach-Colmez spaces introduced by Colmez, and we explain the precise
relationship with the category of coherent sheaves on the Fargues-Fontaine
curve. One goes from one category to the other by changing the t-structure on
the derived category. Along the way, we obtain a description of the pro-\'etale
cohomology of the open disk and the affine space, of independent interest.
