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Epistemology - m a t h 4 w i s d o m - g m a i l
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Introduction E9F5FC Questions FFFFC0 Software |
- What does it mean to multiply polynomials?
- 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. |

This page was last changed on October 22, 2019, at 09:49 PM