2019/03/01 by Simon Forest, Forest, Simon
Computer Science · #Category Theory (math.CT) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · doi:10.48550/arxiv.1903.00282
openalex publication_date 2019/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we relate the three main formalisms for the notion of pasting diagram in strict ω-categories: Street's parity complexes, Johnson's pasting schemes and Steiner's augmented directed complexes. In the process, we show that the axioms of parity complexes and pasting schemes are not strong enough for them to correctly represent pasting diagrams, and we do so by providing a counter-example. Then, we introduce a new formalism, called torsion-free complexes, which aims at encompassing the three other ones. We prove its correctness by providing a detailed proof that an instance induces a free ω-category. Next, we prove that the three other formalisms can be embedded in some sense in the new one. Finally, we show that there are no other embedding between these four formalisms.