Simplicial Set

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External reading guide · Graduate

A simplicial set is a contravariant functor from the simplex category to sets. Read the order-preserving maps as operations on simplices, keeping degenerate simplices as part of the data.

Before opening the references

Category · contravariant functor · function between sets

Where to read

  1. Start here: Kerodon — Simplicial Sets

    Jacob Lurie · Online reference · English · Free full text

    §1.1, Definitions 1.1.0.2 (simplex category), 1.1.0.4 (simplicial object), and 1.1.0.6 (simplicial set; tag 000H)

    Source page · Checked 2026-10-16

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