Definition 1.2.1.1. Let $S_{}$ be a simplicial set and let $S'_{} \subseteq S_{}$ be a simplicial subset of $S_{}$ (Remark 1.1.0.14). We will say that $S'_{}$ is a summand of $S_{}$ if the simplicial set $S_{}$ decomposes as a coproduct $S'_{} \coprod S''_{}$, for some other simplicial subset $S''_{} \subseteq S_{}$.
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