Definition 14.8.1. Let \mathcal{C} be a category. Let U, V, W be simplicial objects of \mathcal{C}. Let a : U \to V, b : U \to W be morphisms. Assume the pushouts V_ n \amalg _{U_ n} W_ n exist in \mathcal{C}. The pushout of V and W over U is the simplicial object V\amalg _ U W defined as follows:
(V \amalg _ U W)_ n = V_ n \amalg _{U_ n} W_ n,
d^ n_ i = (d^ n_ i, d^ n_ i), and
s^ n_ i = (s^ n_ i, s^ n_ i).
In other words, V\amalg _ U W is the pushout of the presheaves V and W over the presheaf U on \Delta .
Comments (2)
Comment #138 by Pieter Belmans on
Comment #140 by Johan on