nLab fat Delta category

Definition

The fat Delta category $\underline{\Delta}$ is the category whose objects are the epimorphisms $g:X \twoheadrightarrow Y$ in the simplex category and whose morphisms are commutative squares in the simplex category whose vertical arrows are epimorphisms and horizontal top arrow is a monomorphism.

$$\array{& X & \overset{f}\hookrightarrow & Z & \\ g & \downarrow &&\downarrow & g'\\ &Y & \underset{f'}\rightarrow& W & \\ }$$

Related concepts

• simplex category

References

• Joachim Kock. Weak identity arrows in higher categories. In: International Mathematics Research Papers 2006 (2006), pp. 1–54. (doi:10.1155/IMRP/2006/69163)

• Nicolai Kraus, Christian Sattler, Space-Valued Diagrams, Type-Theoretically (Extended Abstract) (arXiv:1704.04543)

• Simona Paoli, Weakly globular double categories and weak units (arXiv:2008.11180)

• Tom de Jong, Nicolai Kraus, Simona Paoli, Stiéphen Pradal, A study of Kock’s fat Delta (arXiv:2503.10963)