Higher fundamental functors for simplicial sets
Marco Grandis (2001)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Schuhmacher, Frank (2004)
Homology, Homotopy and Applications
Teimuraz Pirashvili (2000)
Annales scientifiques de l'École Normale Supérieure
Pierre Cartier (1983/1984)
Séminaire Bourbaki
Pitsch, Wolfgang, Scherer, Jérôme (2004)
Homology, Homotopy and Applications
J. Barja, C. Rodriguez (1990)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Khusainov, A.A. (2008)
Sibirskij Matematicheskij Zhurnal
Robert J. MacG. Dawson (1990)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Mirzaii, B., van der Kallen, W. (2002)
Documenta Mathematica
Pavle V. M. Blagojević (2001)
Publications de l'Institut Mathématique
Rudolf Fritsch, Dana May Latch (1981)
Mathematische Zeitschrift
Antonio R. Garzon, Jesus G. Miranda (1997)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Marek Golasiński (1997)
Annales de l'institut Fourier
We generalize the results by G.V. Triantafillou and B. Fine on -disconnected simplicial sets. An existence of an injective minimal model for a complete -algebra is presented, for any -category . We then make use of the -category associated with a -simplicial set to apply these results to the category of -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent -simplicial set by means of its injective minimal model.
Luzius Grünenfelder (1980)
Commentarii mathematici Helvetici
Barmak, Jonathan Ariel, Minian, Elias Gabriel (2007)
Journal of Homotopy and Related Structures
Agustí Roig (1993)
Publicacions Matemàtiques
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....
Everaert, T., Kieboom, R.W., Van der Linden, T. (2005)
Theory and Applications of Categories [electronic only]
Jolanta Słomińska (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.
Bourn, Dominique (2000)
Theory and Applications of Categories [electronic only]
Carlos Ruiz Salguero, Joaquín Luna Torres (1982)
Collectanea Mathematica