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By Laenas Gifford Weld

The purpose of the writer of the current paintings has been to strengthen the speculation of Determinants within the least difficult attainable demeanour. nice care has been taken to introduce the topic in the sort of approach that any reader having an acquaintance with the foundations of uncomplicated Algebra can intelligently persist with this improvement from the start. The final chapters needs to be passed over by means of the coed who's now not acquainted with the Calculus, and a similar is to be acknowledged in connection with a few few of the previous articles ; yet in no case will the continuity of the path be tormented by such omissions.

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8). e. 3) TI (X) ~H ab n n (1) provenant de la fUche canonique (XCU). x(U» ---+«l'*X)(l'*U), Cftx)(f'*U». 2. Le théorème de Whitehead. 1. 2) i

1», le foncteur de localisation Hot. 20). 13. Variantes relatives. 1. B E ob Simpl (T). Nous dirons qu'une flèche de si la flèche sous-jacente de rel. à Simpl(T)/B SimpleT) est un quasi-isomorphisme en est un. Nous appellerons catégorie dérivée de T S, et nous noterons Simpl(T)/B par rapport aux quasi-isomorphismes. (T,S) Simpl (T) lB B-homotopie de flèches de la catégorie localisée de Hot. 6). 3), que Hot. (T,S) est localisée de D. (T,B) B-homotopismes, et par suite que par rapport aux quasi-isomorphismes (avec l'extension évidente de la terminologie).

7». 1,2, Faisceautisation. A partir de maintenant, on se fixe un topos T , dont on note e l'objet final. e. un objet simplicial de de T • Un point-base de Xo(e} ; si U est un objet de une section de (X,x) ,où X au-dessus de o X est une flèche T U (X,x) X au-dessus de U est Un faisceau simplicial pointé est un couple x un point-base de un faisceau simplicial pointé. e. 1. 1). 4). On dit que X est ~ si l'on a un faisceau de groupes, abéliens pour (X,x) TTo(X) n ~ ~ e . Pour 2 . 1), dans la catégorie à homotopie près correspondante Hotsimpl(T,).

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