The category of simplicial –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
–local
homotopy theory of simplicial presheaves and the homotopy theory of simplicial
–modules
by Quillen adjunctions. We study the comparison with the
–local
homotopy theory of simplicial presheaves in the special case where
is a presheaf of algebraically closed (or perfect) fields. If
is a presheaf of algebraically closed fields, we show that the
–local homotopy
category of simplicial presheaves embeds fully faithfully in the homotopy category of simplicial
–coalgebras.
Keywords
coalgebras, simplicial presheaves, local homotopy theory,
combinatorial model category
