Warning 7.4.5.19 (Fake Colimits). In the formulation of Proposition 7.4.5.18, the assumption that $\operatorname{\mathcal{C}}$ is $\kappa $-small cannot be omitted. If $\operatorname{\mathcal{C}}$ is “too large” in comparison with $\lambda $, then it is possible to have a colimit diagram $\overline{\mathscr {F}}: \operatorname{\mathcal{C}}^{\triangleleft } \rightarrow \operatorname{\mathcal{QC}}^{< \lambda }$ which does not satisfy condition $(\ast )$ of Theorem 7.4.5.11 (see Warning 7.4.3.9). In this case, $\overline{\mathscr {F}}$ does not remain a colimit diagram in $\operatorname{\mathcal{QC}}^{< \mu }$ for $\mu \gg \lambda $.
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