English

Internal groupoids as involutive-2-links

Category Theory 2023-05-24 v1

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.

Keywords

Cite

@article{arxiv.2305.13537,
  title  = {Internal groupoids as involutive-2-links},
  author = {Nelson Martins-Ferreira},
  journal= {arXiv preprint arXiv:2305.13537},
  year   = {2023}
}