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CATEGORY OF STRIP FOLDING IN TERMS OF A BOOLEAN MATRIX REPRESENTATION
Keywords:
origami, category theory, strip foldingDOI:
https://doi.org/10.17654/0972555522032Abstract
Strip folding, known as the map folding in the $1 \times n$ 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.
Received: August 29, 2022
Accepted: September 28, 2022
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Yiyang Jia and Thomas Hull, A transformation from map folding to Boolean matrix algebra, Discrete and Computational Geometry, Graphs, and Games: 24th Japanese Conference, JCDCGGG 2022.
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