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I’d not bumped into this concept before (WP link). But it would be nice to have some n-sights on this.
It does seem very ’crossed-module-y’, it could be that two groups are isoclinic if some natural crossed modules (or higher versions) built from them are weakly equivalent. Unfortunately the WP page looks like it should say an isoclinism should be built from a specific map, rather than just existence of some abstract isos with some confusingly written condition.
There is some link with the universal commutator relations that come with the tensor square construction of Ronnie, but I am not sure what the actual link is.
…. and perhaps Urs will be interested in this.
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