It is claimed that in the model category of simplicial sets (with usual model structure), a trivial fibration $X \to Y$ has a section, which is a trivial cofibration.
Now, I see that there is a section, by using lifting property with $\emptyset \to Y$ on the left (all objects are cofibrant!). I see from 2-out-of-3 that this section is an equivalence. How can I see that it is a cofibration?
Thank you, Sasha