NDLI: Formalization of a normalization theorem in simplicial topology

Content Provider	Springer Nature Link
Author	Lambán, Laurea Martín Mateos, Francisco Jesús Rubio, Julio Ruiz Reina, José Luis
Copyright Year	2012
Abstract	In this paper we present a complete formalization of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. Even if the Normalization Theorem is usually stated as a higher-order result (with a Category Theory flavor) we manage to give a first-order proof of it. To this aim it is instrumental the introduction of an algebraic data structure called simplicial polynomial. As a demonstration of the validity of our techniques we developed a formal proof in the ACL2 theorem prover.
Ending Page	37
Page Count	37
Starting Page	1
File Format	PDF
ISSN	10122443
e-ISSN	15737470
Journal	Annals of Mathematics and Artificial Intelligence
Issue Number	1
Volume Number	64
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-01-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Automated reasoning Simplicial sets and complexes Formalization of mathematics ACL2 Computer Science Artificial Intelligence (incl. Robotics) Normalization theorem Mathematics Theorem proving (deduction, resolution, etc.) Statistical Physics, Dynamical Systems and Complexity Algebraic topology
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence

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