Kan Complex

← Encyclopedia

External reading guide · Graduate

A Kan complex is a simplicial set in which every horn admits a filler. Check outer as well as inner horns to distinguish this condition from the inner-horn condition for quasicategories.

Before opening the references

Simplicial Set · Homotopy of Maps · groupoid

Where to read

  1. Start here: Kerodon — Kan Complexes

    Jacob Lurie · Online reference · English · Free full text

    §1.2.5, Definition 1.2.5.1 (tag 002H), including all horns with n > 0 and 0 ≤ i ≤ n

    Checked 2026-10-16

Continue from here

Category Theory in the library · Preparation and skip guidance

Suggest an edit · Report a correction

Original orientation: CC BY-SA 4.0. Linked texts retain their own licences.