A binary operation on the class of coherently diagonal complexes

TL;DR

This paper proves that the horizontal composition of coherently diagonal complexes results in another coherently diagonal complex, using mathematical induction to establish the binary operation property.

Contribution

It introduces a proof that horizontal composition preserves the coherently diagonal property in complexes, confirming it as a binary operation.

Findings

Horizontal composition preserves the coherently diagonal property.

Embedding two such complexes yields a coherently diagonal complex.

The proof employs mathematical induction.

Abstract

We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.