Abstract: Strip folding, known as the map folding in the case, derives from a classical flat-foldability decision problem in the field of computational origami. In this manuscript, different from the existing computational and algorithmic methodology, we investigate the strip folding using abstract algebraic language and then characterize it from a categorical viewpoint. We first present a boolean matrix description of strip folding, based on which we then build the category of strip folding. This category gives rise to a natural meet semi-lattice structure. Furthermore, in this category, every product exists. We use the right adjoint functor of the diagonal functor to define these products. Furthermore, the definition of products can be used to build a Grothendieck topology on the space of flatly folded states. Our result shows that the analysis of strip folding can be associated with contemporary mathematical methodologies such as category theory and algebraic geometry.
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Keywords and phrases: origami, category theory, strip folding.
Received: August 29, 2022; Accepted: September 28, 2022; Published: October 11, 2022
How to cite this article: Yiyang Jia and Jun Mitani, Category of strip folding in terms of a boolean matrix representation, JP Journal of Algebra, Number Theory and Applications 58 (2022), 19-36. http://dx.doi.org/10.17654/0972555522032
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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