Multiplicity of a space over another space

Details Multiplicity of a space over another space Multiplicity of a space over another space

2011-01-10

arxiv.org/abs/1101.1700v2

Mathematics

Category Theory

22 pages, 3 figures, some references added, to appear in J. Math. Soc. Japan

Scientific paper

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 $R$-modules and $R$-linear maps over a principal ideal domain $R$, and the neighbourhood category of oriented knots in the 3-sphere.

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