Simplicial presheaves of coalgebras

Raptis, George

doi:10.2140/agt.2013.13.1967

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Simplicial presheaves of coalgebras

George Raptis

Algebraic & Geometric Topology 13 (2013) 1967–2000

DOI: 10.2140/agt.2013.13.1967

Abstract

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 theory 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.

Keywords

coalgebras, simplicial presheaves, local homotopy theory, combinatorial model category

Mathematical Subject Classification 2010

Primary: 18F20, 18G30, 55U35, 16T15

References

Publication

Received: 24 September 2012

Accepted: 15 January 2013

Published: 29 May 2013

Authors

George Raptis
Universität Osnabrück Institut für Mathematik Albrechtstrasse 28a D-49076 Osnabrück Germany

Volume 13, issue 4 (2013)