Generalized Penon Involutive Weak Globular Higher Categories

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Published: Sep 25, 2024
Keywords:
Involutive Category Higher Category Monad

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Paratat Bejrakarbum
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani, Thailand
Paolo Bertozzini
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani, Thailand

Abstract

This research examines a generalization of the concept of an involutive weak globular 𝜔-category through Penon’s approach. We first introduce the notion of a globular cone, then equip it with compositions, identities, and self-duality. Next, a free reflexive self-dual globular-cone 𝜔-magma and a free strict involutive globular-cone 𝜔-category along with a specified contraction over a given globular cone are established. An algebra for the monad induced by the free-forgetful adjunction arising from the previously constructed structure naturally defines an involutive weak globular-cone 𝜔-category. We finally provide crucial examples of involutive weak globular-cone 𝜔-categories.

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How to Cite
Bejrakarbum, P., & Bertozzini, P. (2024). Generalized Penon Involutive Weak Globular Higher Categories. Science & Technology Asia, 29(3), 10–24. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/250738
Issue
Vol.29 No.3 (July-September 2024)
Section
Physical sciences
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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