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So maybe here’s a better place: how should we relate what you’ve written to center of an infinity-group? What’s a not-necessarily-central higher extension?
Ah, of course we have infinity-group extension with a section on central such.
added these words at the beginning:
In higher algebra a higher central extension of some algebraic object should be a higher analog of a central extension, hence a higher extension by something in the higher analog of the center. What exactly “higher center” should mean is subject to some choices, see for instance center of an ∞-group.
But there is an easily identified sub-class of higher extensions that should definitely count as higher central extensions:
re #3, thanks, will cross-link now
How about ’Higher central extensions and cohomology’ by Diana Rodelo and Tim van der Linden? (see here.) There are a few papers following on from Janeldize’s earler work on double central extensions. (I am ‘on the move’ at the moment so will not have a chance to check up on these.)
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