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Computing with finitely presented representations of a category

Banff International Research Station for Mathematical Innovation and Discovery

In the same way that a matrix of homogeneous polynomials gives rise to a graded module, a matrix over a category gives rise to a "graded module" where the objects of the category provide the degrees, and the arrows provide the monomials (appearing in linear combinations as entries in the matrix). When the category is combinatorial in nature, such a matrix may be entered into a computer. Using examples from combinatorics, geometry, and topology, I will demonstrate a computer program that takes a matrix over the category of finite sets and returns its Hilbert series.

Mathematics; Commutative rings and algebras; Category theory; homological algebra; Commutative algebra

video/mp4

Author affiliation: University of Michigan

2016-10-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59391

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/