Size Functions from a Categorical Viewpoint

  title={Size Functions from a Categorical Viewpoint},
  author={Francesca Cagliari and Massimo Ferri and Paola Pozzi},
A new categorical approach to size functions is given. Using this point of view, it is shown that size functions of a Morse map, f : M→ R can be computed through the 0-dimensional homology. This result is extended to the homology of arbitrary degree in order to obtain new invariants of the shape of the graph of the given map. Mathematics Subject Classifications (2000): 68T10, 57R70, 55U99. 
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