nLab prism

This article is on prisms as a geometric shape. A different sense of ‘prism’ is studied in prismatic cohomology.

Overview

The category of prisms is one of the geometric shapes for higher structures. The resulting presheaves of sets are known as multisimplicial sets?. These were used by Laures and McClure in their work on Quinn spectra?.

Definition

The category of $n$-fold prisms is the $n$-fold product of the category of simplices $\Delta$.

Presheaves on this category are known as $n$-fold multisimplicial sets.

Restricting to injective maps of simplices, we get $n$-fold multisemisimplicial sets.

Related notions

• geometric shapes for higher categories

References

• Gerd Laures?, James E. McClure,

  Commutativity properties of Quinn spectra, (arXiv:1304.4759)

• Gerd Laures?, James E. McClure,

  Multiplicative properties of Quinn spectra, (arXiv:0907.2367)