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arXiv · 2305.13537

Internal groupoids as involutive-2-links

Nelson Martins-Ferreira
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Abstract

Regardless of its environment, the category of internal groupoids is shown to be equivalent to the full subcategory of involutive-2-links that are unital and associative. The new notion of involutive-2-link originates from the study of triangulated surfaces and their application in additive manufacturing and 3d-printing. Thus, this result establishes a bridge between the structure of an internal groupoid and an abstract triangulated surface. An example is provided which can be thought of as a crossed-module of magmas rather than groups.

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Nelson Martins-Ferreira. 2023-05-22. Internal groupoids as involutive-2-links. https://arxiv.org/abs/2305.13537

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