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Digital H-spaces and actions in the pointed digital homotopy category

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Abstract

We apply fundamental ideas from algebraic topology in mathematics to the digital world in computer science. We develop digital H-spaces and digital H-functions between the digital H-spaces with digital multiplications, and construct a necessary and sufficient condition for a digital H-space (or a digital homotopy associative H-space, a digital homotopy commutative H-space, or a digital H-group) to satisfy certain conditions in the category of magmas or a category of algebraic objects such as semigroups, monoids, or groups. We also investigate an action on the set of pointed digital homotopy (associative or commutative) multiplications to create new digital homotopy (resp., associative or commutative) multiplications.

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Acknowledgements

The author is grateful to the anonymous referee(s) for a careful reading and many helpful suggestions that improved the quality of this paper.

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  1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do, 54896, Republic of Korea

    Dae-Woong Lee

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Correspondence to Dae-Woong Lee.

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This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIT) (No. 2018R1A2B6004407)

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Lee, DW. Digital H-spaces and actions in the pointed digital homotopy category. AAECC 31, 149–169 (2020). https://doi.org/10.1007/s00200-019-00398-8

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  • DOI: https://doi.org/10.1007/s00200-019-00398-8

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