Multiplicity of a space over another space

  title={Multiplicity of a space over another space},
  author={Kouki Taniyama},
  journal={arXiv: Category Theory},
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. We define and study several multiplicities in the category of topological spaces and continuous maps, the category of groups and homomorphisms, the category of finitely generated… Expand

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