Retract conjecture on a sublattice of monoidal posets

Kato, Ryo

doi:10.1090/proc/16221

Retract conjecture on a sublattice of monoidal posets
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by Ryo Kato;

Proc. Amer. Math. Soc. 151 (2023), 3157-3167

DOI: https://doi.org/10.1090/proc/16221

Published electronically: March 31, 2023

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Abstract:

Hovey and Palmieri [The structure of the Bousfield lattice, Amer. Math. Soc., Providence, RI, 1999] proposed the retract conjecture on the Bousfield lattice of the stable homotopy category. The author, Shimomura and Tatehara [Publ. Res. Inst. Math. Sci. 50 (2014), pp. 497–513] defined the notion of monoidal posets as a generalization of the Bousfield lattice. In this paper, we prove that an analogue of the retract conjecture holds on a sublattice of monoidal posets.

References

W. G. Dwyer and J. H. Palmieri, The Bousfield lattice for truncated polynomial algebras, Homology Homotopy Appl. 10 (2008), no. 1, 413–436. MR 2426110, DOI 10.4310/HHA.2008.v10.n1.a18
Mark Hovey and John H. Palmieri, The structure of the Bousfield lattice, Homotopy invariant algebraic structures (Baltimore, MD, 1998) Contemp. Math., vol. 239, Amer. Math. Soc., Providence, RI, 1999, pp. 175–196. MR 1718080, DOI 10.1090/conm/239/03601
Ryo Kato, Katsumi Shimomura, and Yutaro Tatehara, Generalized Bousfield lattices and a generalized retract conjecture, Publ. Res. Inst. Math. Sci. 50 (2014), no. 3, 497–513. MR 3262447, DOI 10.4171/PRIMS/142
Tetsusuke Ohkawa, The injective hull of homotopy types with respect to generalized homology functors, Hiroshima Math. J. 19 (1989), no. 3, 631–639. MR 1035147