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数学

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Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

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Introduction E9F5FC

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Software


  • What does it mean to multiply polynomials?

Readings

Morphisms of the simplex

  • Power symmetric function {$p_k(x_1, \dots , x_n)$}: one morphism from each simplex {$[k-1]$} to every vertex of {$[n-1]$}.
  • Elementary symmetric function {$p_k(x_1, \dots , x_n)$}: one morphism for every subsimplex.
  • Homogeneous symmetric function {$p_k(x_1, \dots , x_n)$}: one morphism for every monotone function (way of building up).
  • Monomial symmetric function?

Compare these types of morphisms with those of various categories:

  • Inclusion defines morphism for the category of the open sets of a topological space. This space is important for defining a topological presheaf {$C^{op}\rightarrow \mathrm{Top}$}.

Thus we can think of elementary symmetric functions as defining a "topological" perspective on the simplex.

SymmetricFunctionsInCategoryTheory


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Puslapis paskutinį kartą pakeistas 2019 balandžio 17 d., 15:01
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