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.

中文翻译：

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指向数字同伦范畴中的数字 H 空间和动作

我们将数学中代数拓扑的基本思想应用于计算机科学中的数字世界。我们开发了数字 H 空间和数字 H 空间之间的数字 H 函数与数字乘法，并构造了数字 H 空间（或数字同伦关联 H 空间，数字同伦可交换 H-空间或数字 H 群）以满足岩浆类别或代数对象类别（如半群、幺半群或群）中的某些条件。我们还研究了对一组有针对性的数字同伦（关联或交换）乘法的操作，以创建新的数字同伦（相应地，关联或交换）乘法。