2023/05/22 by Martins-Ferreira, Nelson
#08C05 #18D35 #18D40 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.13537
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.