Partial Frobeniuses via black magic

An essential piece of structure on cohomologies of  shtukas is the action of partial Frobenius's  (equivarince with respect to geometric Frobenius 

endomorphisms along each copy of  in ). We will recall the usual construction, and then explain that it follows more or less automatically

from the formalism of categorical trace taken in the category , DGCat_{alg-geom} introduced by Beilinson and Drinfeld.