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A braided 3-group is a braided ∞-group which is a 3-group. For a 3-group, a braiding on it is the following equivalent structure
For a commutative ring, and the braided monoidal 2-category of -algebras, bimodules and bimodule homomorphism, the maximal 3-group
inside is a braided 3-group. Its homotopy groups are the Brauer group, the Picard group and the group of units of . See at Brauer group – Relation to category of modules for more on this.
braided 3-group
As a special case of k-tuply groupal n-groupoids the notion is at least implicit in:
In the generality of braided ∞-group stacks the notion appears in:
Last revised on July 21, 2021 at 15:10:28. See the history of this page for a list of all contributions to it.