The Globe Category

The Globe Category $G$ is the category generated by maps $\sigma:[n]\to[n+1]$ and $\tau:[n]\to[n+1]$, subject to the following equations:

• $\sigma\circ\sigma=\tau\circ\sigma$
• $\tau\circ\tau=\sigma\circ\tau$

The intuition here is that $\sigma$ and $\tau$ encode the geometry of source and target maps.

References

• https://ncatlab.org/nlab/show/globe+category