Multiplicity of a space over another space
Category Theory
2015-03-17 v3 Commutative Algebra
Group Theory
Geometric Topology
Abstract
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 -modules and -linear maps over a principal ideal domain , and the neighbourhood category of oriented knots in the 3-sphere.
Keywords
Cite
@article{arxiv.1101.1700,
title = {Multiplicity of a space over another space},
author = {Kouki Taniyama},
journal= {arXiv preprint arXiv:1101.1700},
year = {2015}
}
Comments
22 pages, 3 figures, some references added, to appear in J. Math. Soc. Japan, Proof of Proposition 2.4 (3) corrected