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つづき
Introduction
Our subject starts with homology, homomorphisms, and tensors.
Homology provides an algebraic "picture" of topological spaces,
assigning to each space X a family of abelian groups H,(X), . . . , H,(X),
. . . , to each continuous map f : X+Y a family of group homomorphisms
f,: H,(X) +H, (Y). Properties of the space or the map can often be
effectively found from properties of the groups H, or the homomorphisms
f,. A similar process associates homology groups to other Mathematical
objects; for example, to a group nor to an associative algebra A. Homology in all such cases is our concern.
Complexes provide a means of calculating homology. Each %-dimensional "singular" simplex T in a topological space X has a boundary
consistini of singular simplices of dimension .n- 1.
Chapter I . Modules. Diagrams. and Functors .............. 8
6 . The Functor Hom .....
7 . Categories ........
8 . Functors .........
Bibliography
GROTHENDIECK, A. : Sur quelques Points d'Alg8bre Homologique. Tohoku Math. J.
9, lie221 (1957). 1x.2; 1x.4; x11.8
- (with J. DIEUDONN*) : l&ments de Mometrie Algebrique. I, 11. Pub. Math.
Inst. des Hautes Etudes. Paris 1960, 1961. Nos. 4 and 8. 1.8
URLﾘﾝｸ(www.maths.ed.ac.uk)
Andrew Ranicki’s Homepage
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