## MODULES IN MONOIDAL MODEL CATEGORIES (2006)

Citations: | 3 - 0 self |

### BibTeX

@MISC{Lewis06modulesin,

author = {L. Gaunce Lewis and Jr. and Michael A. Mandell},

title = {MODULES IN MONOIDAL MODEL CATEGORIES},

year = {2006}

}

### OpenURL

### Abstract

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

### Citations

377 | Basic concepts of enriched category theory, volume 64 - Kelly - 1982 |

191 | Symmetric spectra
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(Show Context)
Citation Context ...eir underlying object in M semicofibrant. Although the we do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra =-=[3, 4, 9]-=- and equivariant spectra on complete universes [7, 8, 10] as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the... |

145 | Algebras and modules in monoidal model categories
- Schwede, Shipley
(Show Context)
Citation Context ...at the homotopy category HoM inherits a symmetric monoidal structure and that the localization functor is (lax) symmetric monoidal. Schwede and Shipley began the study of monoidal model categories in =-=[12]-=-. There, they provide good criteria for the categories of modules and algebras over a monoid A in M to inherit closed model structures from M. The purpose of this paper is to study the existence and b... |

118 |
modules, and algebras in stable homotopy theory
- Rings
- 1997
(Show Context)
Citation Context ...eir underlying object in M semicofibrant. Although the we do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra =-=[3, 4, 9]-=- and equivariant spectra on complete universes [7, 8, 10] as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the... |

114 | Model categories of diagram spectra
- Mandell, May, et al.
(Show Context)
Citation Context ...eir underlying object in M semicofibrant. Although the we do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra =-=[3, 4, 9]-=- and equivariant spectra on complete universes [7, 8, 10] as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the... |

68 |
Model categories, volume 63 of Mathematical Surveys and Monographs
- Hovey
- 1999
(Show Context)
Citation Context ...d like to thank Brooke Shipley and Andrew Blumberg for helpful comments. 2. Monoidal model categories This section reviews the terminology and basic theory of monoidal model categories from [12] (and =-=[5]-=-). The definition of a monoidal model category involves constraints on the interaction of the model structure with the closed symmetric monoidal structure. The imposed conditions suffice to ensure tha... |

61 | Equivariant orthogonal spectra and S-modules
- Mandell, May
(Show Context)
Citation Context ...e do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra [3, 4, 9] and equivariant spectra on complete universes =-=[7, 8, 10]-=- as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the semicofibrancy hypotheses of the theorems of the introdu... |

53 |
Homotopy theories and model categories
- Dwyer, Spaliński
- 1995
(Show Context)
Citation Context ...hment Axiom (Enr), proves the claim about [−, −]. � Parts (d) and (e) of this proposition indicate that ∧ and [−, −] satisfy Quillen’s criterion (Proposition 1 in [11, p. I.4.2] or Proposition 9.3 in =-=[1]-=-) for the existence of a left derived functor �∧ and a right derived functor [−, −], respectively. Moreover, these derived functors can be constructed so that X �∧ Y = X ∧ Y and [Y, Z ] = [Y, Z] whene... |

33 | Homotopy limit functors on model categories and homotopical categories, volume 113 - Dwyer, Hirschhorn, et al. - 2004 |

17 | Homotopical algebra, volume 43 - Quillen - 1967 |

5 |
Equivariant symmetric spectra. Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic
- Mandell
- 2004
(Show Context)
Citation Context ...e do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra [3, 4, 9] and equivariant spectra on complete universes =-=[7, 8, 10]-=- as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the semicofibrancy hypotheses of the theorems of the introdu... |

2 |
Equivariant universal coefficient and Künneth spectral sequences
- Mandell
(Show Context)
Citation Context ...e do not know of a general principle that would imply the second property, it holds in all presently known monoidal model categories of spectra [3, 4, 9] and equivariant spectra on complete universes =-=[7, 8, 10]-=- as well as the most common monoidal model categories coming from algebra. The purpose of this section is to indicate specifically which of the semicofibrancy hypotheses of the theorems of the introdu... |