higher category theory
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A Gray-Groupoid is a semistrict algebraic model for a 3-groupoid:
it is a Gray-category – a semistrict 3-category – in which every k-morphism is invertible.
Gray-groupoids are related to 2-crossed complexes and 2-crossed modules as strict 2-groupoids are related to crossed complexes.
A Gray groupoid with a single object is the delooping of a Gray group.