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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 17th 2019

• Luis Scoccola, Nilpotent Types and Fracture Squares in Homotopy Type Theory (arXiv:1903.03245)
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 30th 2020

• Peter Hilton, Nilpotency in group theory and topology, Publicacions de la Secció de Matemàtiques Vol. 26, No. 3 (1982), pp. 47-78 (jstor:43741908)
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 30th 2020

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 15th 2020

I have added the following under “Examples”:

Directly from the definition we have that:

and more generally

As a special case of this

and thus

• every loop space is nilpotent

(since all its connected components are homotopy equivalent to the unit component, which is a connected H-space).

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 15th 2020

also: