Basic Bundle Theory and K-Cohomology Invariants pp 303-322 | Cite as
Stacks and Gerbes
Chapter
A basic structure in mathematics for the study of a space X is to give to each open set an object A(U) in a category \(\mathcal{c}\) together with restriction morphisms \(r_{V, U}:A(U)\to A(V)\) for \(V\subset U\) satisfying \(r_{U,U}\) is the identity and the composition property . Such a structure is called a presheaf with values in \(\mathcal{c}\).
$$r_{W,U}=r_{W,V}r_{V, U}\qquad {\rm for} \qquad W\subset V\subset U\,.$$
Keywords
Open Covering Universal Property Full Subcategory Principal Bundle Left Adjoint
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© Springer-Verlag Berlin Heidelberg 2008