Minimal resolutions and other minimal models.

Roig, Agustí. "Minimal resolutions and other minimal models.." Publicacions Matemàtiques 37.2 (1993): 285-303. <http://eudml.org/doc/41535>.

@article{Roig1993,
abstract = {In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes. The others follow by a caracterization of minimal objects in bifibred categories.},
author = {Roig, Agustí},
journal = {Publicacions Matemàtiques},
keywords = {Homotopía; Categorías; Functores; KS-extensions; minimal models; weak equivalences; model category; homotopy category; minimal resolutions; minimal fiber spaces},
language = {eng},
number = {2},
pages = {285-303},
title = {Minimal resolutions and other minimal models.},
url = {http://eudml.org/doc/41535},
volume = {37},
year = {1993},
}

TY - JOUR
AU - Roig, Agustí
TI - Minimal resolutions and other minimal models.
JO - Publicacions Matemàtiques
PY - 1993
VL - 37
IS - 2
SP - 285
EP - 303
AB - In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes. The others follow by a caracterization of minimal objects in bifibred categories.
LA - eng
KW - Homotopía; Categorías; Functores; KS-extensions; minimal models; weak equivalences; model category; homotopy category; minimal resolutions; minimal fiber spaces
UR - http://eudml.org/doc/41535
ER -