Higher Fundamental Functors for Simplicial Sets
نویسنده
چکیده
On introduit une théorie d'homotopie combinatoire pour le topos des ensembles simpliciaux symétriques (préfaisceaux sur les cardinaux finis positifs), en étendant une théorie développée pour les complexes simpliciaux [11]; comme avantage essentiel de cette extension, le groupoïde fondamental devient l'adjoint à gauche d'un foncteur nerf symétrique et préserve les colimites, une propriété forte de van Kampen. On a des résultats analogues en toute dimension ≤ ω. On développe aussi une notion d'homotopie orientée pour les ensembles simpliciaux ordinaires, avec un foncteur n-catégorie fondamentale adjoint à gauche du n-nerf. Des constructions similaires peuvent être données dans plusieurs catégories de préfaisceaux.
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