Notation 3.2.2.1. Let $B$ be a simplicial set and let $A \subseteq B$ be a simplicial subset. We let $B/A$ denote the pushout $B \coprod _{A} \{ q\} $, formed in the category of simplicial sets. We regard $B/A$ as a pointed simplicial set, with base point given by the vertex $q$.
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