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HEYTING ALGEBRA IN FLAT ORIGAMI
Keywords:
Heyting algebra, origami, flat-foldDOI:
https://doi.org/10.17654/0972555524023Abstract
This study utilizes category theory to enhance the understanding of flat-fold origami, focusing on the structural characteristics and representation of self-intersections within categorical definitions. We introduce the category of flat states $\mathscr{C}$ and its skeleton category [ $\mathscr{C}]$, based on permutation equivalence. We explored the localized subcategories $\mathscr{C}_P$ and $[\mathscr{C}]_P$ besides establishing a Heyting algebra structure on $[\mathscr{C}]_P$, proved its lack of a locale structure, confirming that $[\mathscr{C}]_P$ functions as a $(0,1)$-topos but does not qualify as a Grothendieck topos. These findings categorize the domain of flat-fold origami as a category of $(0,1)$-topoi, offering significant theoretical insights for analyzing flat-fold origami.
Received: May 28, 2024
Accepted: July 3, 2024
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