The category of simplicial R-coalgebras over a presheaf of commutative unital
rings on a small Grothendieck site is endowed with a left proper, simplicial,
cofibrantly generated model category structure where the weak equivalences are
the local weak equivalences of the underlying simplicial presheaves. This model
category is naturally linked to the R-local homotopy theory of simplicial
presheaves and the homotopy theory of simplicial R-modules by Quillen
adjunctions. We study the comparison with the R-local homotopy category of
simplicial presheaves in the special case where R is a presheaf of
algebraically closed (or perfect) fields. If R is a presheaf of algebraically
closed fields, we show that the R-local homotopy category of simplicial
presheaves embeds fully faithfully in the homotopy category of simplicial
R-coalgebras.Comment: 24 page
