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SHEAVES OF SETS
GROUP BUNDLES AND SHEAVES OF GROUPS
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abelian group algebraic analytic associated fibre space Aut(E canonically isomorphic cocycle commutative composition law continuous map coordinate maps coordinate transformations corollary corresponding definition denoted equivalence relation exact sequence F into F faithful sheaf fibre bundle fibre space associated fibre space defined functor G operates germs of automorphisms germs of continuous germs of isomorphisms germs of maps group bundle group G hence interior automorphisms inverse image left operators Let F Let G Lie group locally isomorphic map f moreover natural map necessary and sufficient neutre element notion of fibre open covering open sets paracompact quotient regular representation restriction maps section of G sheaf G sheaf of germs sheaf of groups sheaf of left space of structure space with composition space with G space with structure structure group structure of type structure sheaf structure type subset subsheaf of groups system of coordinate topological group topology trivial fibre space X-homomorphism Zariski topology