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      • Bilkent Theses
      • Theses - Department of Mathematics
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      The geometry of sheaves on sites

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      Author(s)
      Parsizadeh, Pejman
      Advisor
      Ünlü, Özgün
      Date
      2021-01
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
      Item Usage Stats
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      Abstract
      In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we introduce the notion of varieties, and show the relationship between certain class of varieties known as diffeologies with the category of smooth manifolds. Along the way, the notion of schemes will be generalized as a variety on symmetric monoidal categories. And we show how a differential geometric construction on a site can be translated to a construction on generalized spaces.
      Keywords
      Sheaves
      Sites
      Geometry
      Permalink
      http://hdl.handle.net/11693/54983
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      • Dept. of Mathematics - Master's degree 128
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