Eilenberg-Steenrod axioms of sheaf cohomology - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T21:37:06Z http://mathoverflow.net/feeds/question/113812 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113812/eilenberg-steenrod-axioms-of-sheaf-cohomology Eilenberg-Steenrod axioms of sheaf cohomology Dan Petersen 2012-11-19T10:52:17Z 2012-11-19T15:09:33Z <p>Cohomology of a space is often defined axiomatically: a cohomology theory is a functor from pairs of spaces to abelian groups satisfying the Eilenberg-Steenrod axioms. Is there a similar characterization of sheaf cohomology, where the domain of the functor is now a category of pairs $(A,X,\mathcal F)$ with $A \subset X$ a pair and $\mathcal F$ an abelian sheaf on $X$ (with the obvious morphisms)?</p> <p>Are there extraordinary sheaf cohomology theories?!</p>