symmetric monoidal (∞,1)-category of spectra
An -space or -algebra in spaces is a space (in the sense of an homotopy type/-groupoid, usually presented by a topological space or a simplicial set) with a multiplication that is associative up to higher homotopies involving up to variables.
An -space is a pointed space.
Same with an -space.
An -space is an H-space.
An -space? is a homotopy associative H-space (but no coherence is required of the associator).
An -space has an associativity homotopy that satisfies the pentagon identity up to homotopy, but no further coherence.
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A3-groupoid?
The notion is originally due to:
Jim Stasheff, Homotopy associativity of H-spaces I, Trans. Amer. Math. Soc. 108 2 (1963) 275-292 [doi:10.2307/1993608]
Jim Stasheff, Homotopy associativity of H-spaces II 108 2 (1963) 293-312 [doi:10.2307/1993609, doi:10.1090/S0002-9947-1963-0158400-5]
Early review:
Last revised on July 5, 2022 at 12:24:31. See the history of this page for a list of all contributions to it.