### Abstract

Given a triple J on the category of (pointed) spaces, one uses the cosimplicial. resolution J . X of a space X, to define the functors J(n)X = Tot(n) J.X. When n = infinity this is known as the completion functor.

We show that when J is a module triple, then the Bousfield-Kan functors J(n) are triples on the homotopy category of spaces. In particular, when E is the spectrum of an S-algebra (or a symmetric spectrum), then the E-completion functor is up to homotopy a triple. (C) 2002 Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 133-157 |

Number of pages | 24 |

Journal | Topology and its Applications |

Volume | 130 |

Issue number | 2 |

Early online date | 8 Nov 2002 |

DOIs | |

Publication status | Published - May 2003 |

### Keywords

- homotopy limits
- triples
- completions

### Cite this

*Topology and its Applications*,

*130*(2), 133-157. https://doi.org/10.1016/S0166-8641(02)00217-1

**Homotopy Limits of Triples.** / Libman, Assaf.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 130, no. 2, pp. 133-157. https://doi.org/10.1016/S0166-8641(02)00217-1

}

TY - JOUR

T1 - Homotopy Limits of Triples

AU - Libman, Assaf

PY - 2003/5

Y1 - 2003/5

N2 - Given a triple J on the category of (pointed) spaces, one uses the cosimplicial. resolution J . X of a space X, to define the functors J(n)X = Tot(n) J.X. When n = infinity this is known as the completion functor.We show that when J is a module triple, then the Bousfield-Kan functors J(n) are triples on the homotopy category of spaces. In particular, when E is the spectrum of an S-algebra (or a symmetric spectrum), then the E-completion functor is up to homotopy a triple. (C) 2002 Elsevier Science B.V. All rights reserved.

AB - Given a triple J on the category of (pointed) spaces, one uses the cosimplicial. resolution J . X of a space X, to define the functors J(n)X = Tot(n) J.X. When n = infinity this is known as the completion functor.We show that when J is a module triple, then the Bousfield-Kan functors J(n) are triples on the homotopy category of spaces. In particular, when E is the spectrum of an S-algebra (or a symmetric spectrum), then the E-completion functor is up to homotopy a triple. (C) 2002 Elsevier Science B.V. All rights reserved.

KW - homotopy limits

KW - triples

KW - completions

U2 - 10.1016/S0166-8641(02)00217-1

DO - 10.1016/S0166-8641(02)00217-1

M3 - Article

VL - 130

SP - 133

EP - 157

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -