Simplicial map

Simplicial map

Topology

Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022

Steve Huntsman, Jimmy Palladino, Michael Robinson

It is rather computationally difficult to study abstract simplicial complexes and simplicial maps directly. It is much easier to work by analogy: transform abstract simplicial complexes into vector spaces and simplicial maps into linear maps. The way we will do this is by way of a construction called simplicial homology. The construction is a two-step process, in which we first transform each abstract simplicial complex into an algebraic construction called a chain complex (schematically depicted in Figure 4.3), and each simplicial map transforms into a chain map. From there, chain complexes and chain maps allow us to compute topological invariants via linear algebra.

A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools

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Journal Information

Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019

Chris Fields, James F. Glazebrook

given by , and secondly, for any choice of splitting, the function (recall ) induces a simplicial map with respect to the Čech nerve

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Topology

A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools