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 Oct21 comment How does the reduced cone look like? Yes, by rail I meant interval. I change the form of question, that's the question I got. We didn't mention topology. Oct21 revised How does the reduced cone look like? Change the form of question Oct20 comment How does the reduced cone look like? Thank you for your help, but I can't use it because I defined Cone(X) as union of all rails between points from X and one external point, the top of Cone. Oct20 asked How does the reduced cone look like? Oct17 comment How to prove that the slice category over a Quillen model category is also a Quillen model category? I'm sorry because I'm not very clear in explaining,english is not my mother language, I'll try to do so now on. Yes,f is weak equivalence between A and B in the base C and slice category is $C/X$. Oct17 comment How to prove that the slice category over a Quillen model category is also a Quillen model category? W.e. is diagram that comutes $h_1=h_2f$ and f is w.e. , $f:A->B, h_1:A->X, h_2:B->X$.Analog for fibration and cofibration Oct17 asked How to show that $\Delta[n]$ isn't Kan fibrant…? Oct17 revised How to prove that the slice category over a Quillen model category is also a Quillen model category? edited title Oct17 comment Morphism is a retraction of another morphism? I'm using slice category, I'm not sure how diagram looks like when f is retraction of g. Actually, I have to prove that slice category is Quillen model category by checking axioms and my stuck with retract axiom. Oct17 asked How to prove that coequalizer is a epimorphism? Oct17 asked Morphism is a retraction of another morphism? Oct16 asked How to prove that the slice category over a Quillen model category is also a Quillen model category? Oct12 awarded Student Oct12 awarded Editor Oct12 revised How to show that wedge sum is coproduct? added 1 characters in body Oct12 asked How to show that wedge sum is coproduct?