Special and general types
Let be a stable (∞,1)-category (or (∞,1)-topos) and a stable coefficient object. For and or () write
for the cohomology of with coefficients in in degree .
Say a morphism in is -local if it induces isomorphisms on all these cohomology groups. Let be the class of all such morphisms.
Then the -cohomology localization of is – if it exists – the localization of an (∞,1)-category of at .
Set theoretic issues in cohomology localization – and their solution using large cardinal axioms such as Vopenka's principle, is discussed in
Carles Casacuberta, Dirk Scevenels, Jeff Smith, Implications of large-cardinal principles in homotopical localization Advances in Mathematics Volume 197, Issue 1, 20 October 2005, Pages 120-139
Joan Bagaria, Carles Casacuberta, A. R. D. Mathias, Jiri Rosicky, Definable orthogonality classes in accessible categories are small (arXiv:1101.2792)
Revised on September 3, 2012 18:09:46
by Urs Schreiber