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Simplicial presheaves of coalgebras

George Raptis

Algebraic & Geometric Topology 13 (2013) 1967–2000

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.

coalgebras, simplicial presheaves, local homotopy theory, combinatorial model category
Mathematical Subject Classification 2010
Primary: 18F20, 18G30, 55U35, 16T15
Received: 24 September 2012
Accepted: 15 January 2013
Published: 29 May 2013
George Raptis
Universität Osnabrück
Institut für Mathematik
Albrechtstrasse 28a
D-49076 Osnabrück