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For questions about simplicial sets, simplicial (co)algebras and simplicial objects in other categories; geometric realization, Dold-Kan correspondence, simplicial resolutions etc.
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A fibration is a map which has the right lifting property with respect to injections that ar...
As mentioned in Motivic Homotopy Theory, an alternative criterion for $X\rightarrow Y$ to be a fibration is that the diagram
$$\require{AMScd}
\begin{CD}
A @>>> X;\\
@VV{i}V @VVV \\
B @>>> Y;
\end{CD} …