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Obvious natural morphisms of sheaves are unique

Reich, Ryan Cohen

Theory and Applications of Categories, Vol. 29, 2014, No. 4, pp 48-99

Arxiv ID: 1307.4678

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  • Nhan đề:
    Obvious natural morphisms of sheaves are unique
  • Tác giả: Reich, Ryan Cohen
  • Chủ đề: Mathematics - Algebraic Geometry ; Mathematics - Category Theory
  • Là 1 phần của: Theory and Applications of Categories, Vol. 29, 2014, No. 4, pp 48-99
  • Mô tả: We prove that a large class of natural transformations (consisting roughly of those constructed via composition from the "functorial" or "base change" transformations) between two functors of the form $\cdots f^* g_* \cdots$ actually has only one element, and thus that any diagram of such maps necessarily commutes. We identify the precise axioms defining what we call a "geofibered category" that ensure that such a coherence theorem exists. Our results apply to all the usual sheaf-theoretic contexts of algebraic geometry. The analogous result that would include any other of the six functors remains unknown. Comment: 52 pages. Final draft, version accepted to TAC
  • Số nhận dạng: Arxiv ID: 1307.4678

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