In this chapter, we develop the basic geometric concepts. In line with the general structure of this text, we use a category theoretical language. While the basic notions of category theory will only be introduced later in Sect. 4.1 , this chapter will already introduce some of the examples of categories that are important in our context.

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Metrics and Riemannian Manifolds

  • Lukas Silvester Barth,
  • Hannaneh Fahimi,
  • Parvaneh Joharinad,
  • Jürgen Jost,
  • Janis Keck

摘要

In this chapter, we develop the basic geometric concepts. In line with the general structure of this text, we use a category theoretical language. While the basic notions of category theory will only be introduced later in Sect. 4.1 , this chapter will already introduce some of the examples of categories that are important in our context.