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http -> https (the question was bumped anyway)
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Martin Sleziak
Martin Sleziak
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I would think -- but this is for the moment a thought, not meant as an authorativeauthoritative answer -- that every notion of cohomology whatsoever has a relative version in this sense.

I am thinking here of the general abstract definition of cohomology as exposed at nLab:cohomologynLab:cohomology. This includes in particular the special case of sheaf cohomologysheaf cohomology as described there in some detail.

What I expect the fully general notion of relative cohomology from this point of view to be I have now briefly indicated at relative cohomologyrelative cohomology. I'd believe this does in particular reproduce the definition given in Emerton's answer.

I would think -- but this is for the moment a thought, not meant as an authorative answer -- that every notion of cohomology whatsoever has a relative version in this sense.

I am thinking here of the general abstract definition of cohomology as exposed at nLab:cohomology. This includes in particular the special case of sheaf cohomology as described there in some detail.

What I expect the fully general notion of relative cohomology from this point of view to be I have now briefly indicated at relative cohomology. I'd believe this does in particular reproduce the definition given in Emerton's answer.

I would think -- but this is for the moment a thought, not meant as an authoritative answer -- that every notion of cohomology whatsoever has a relative version in this sense.

I am thinking here of the general abstract definition of cohomology as exposed at nLab:cohomology. This includes in particular the special case of sheaf cohomology as described there in some detail.

What I expect the fully general notion of relative cohomology from this point of view to be I have now briefly indicated at relative cohomology. I'd believe this does in particular reproduce the definition given in Emerton's answer.

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Urs Schreiber
Urs Schreiber
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I would think -- but this is for the moment a thought, not meant as an authorative answer -- that every notion of cohomology whatsoever has a relative version in this sense.

I am thinking here of the general abstract definition of cohomology as exposed at nLab:cohomology. This includes in particular the special case of sheaf cohomology as described there in some detail.

What I expect the fully general notion of relative cohomology from this point of view to be I have now briefly indicated at relative cohomology. I'd believe this does in particular reproduce the definition given in Emerton's answer.