In the classical theory for coherent sheaves, the only missing piece in the Grothendieck
six-functor formalism picture is j! for an open immersion j. Towards fixing this gap, Deligne
provided a construction of j! by extending the sheaf class to pro sheaves, while Clausen-
Scholze provided another solution by extending the sheaf class to solid modules. In this talk,
I will explain how Deligne’s construction coincides with the Clausen-Scholze construction via
a natural functor, whose restriction to the full subcategory of Mittag-Leffler pro-systems is
fully faithful.