Simplices, face maps, and degeneracy maps

Notation 1.2.10. For \(n \geq 0\), we write \([n]\) for the following linearly ordered set: \[ [n] := \{0 \leq 1 \leq \dots \leq n\}. \] For \(n \geq 1\) and \(0 \leq i \leq n\), we define the face map \(d_i\colon [n-1] \to [n]\) as the unique injective map of posets whose image leaves out \(i\). Similarly we define the degeneracy map \(s_i\colon [n + 1] \to [n]\) as the unique surjective map of posets that hits \(i\) twice.