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THE PL US CONSTRUCTION
THE CLASSIFYING SPACE OF A SMALL CATEGORY
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abelian category abelian group Algebraic K-Theory arrow associated base point BGL(R bijection category of finite central extension classifying space coefficient cohomology coker commutative compactly complex composite construction COROLLARY CW-complex defined denote the category diagram divisor exact category exact functor fibration field follows full subcategory functor f Galois given gives GL(R H-space homology homomorphism homotopy Cartesian homotopy equivalence homotopy fibre homotopy groups homotopy type inclusion induced map injective inverse K-groups lemma Let f localisation sequence long exact sequence map f modules monoidal morphism natural isomorphism natural map natural transformation NDR-pair Noetherian object obtained pair path prime PROOF quotient R-modules ring Serre subcategory sheaf simplicial set simplicial space small categories Spec spectral sequence subgroup subobjects subset suffices to prove surjective Theorem topological spaces trivial unique upto homotopy vector bundle