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Let's consider a diagram $\Phi: \lambda \to \mathcal{T}_*$ $$ X_0 \to X_1 \to \cdots \to X_\xi \to X_{\xi+1} \to \cdots $$ of pointed spaces, indexed by some ordinal $\lambda$, in which each $X_\xi$ ...

I am not an expert, thus I apologize if my question is very naive. Let $\mathsf{M}$ be a model category (I do not assume any functoriality on the factorization), Q1. Is there a reference where it is ...