Timeline for How to show the following two definitions of homotopy monomorphism are equivalent?

7 events

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May 13, 2015 at 18:03	comment	added	Fernando Muro		Warning! Contains self promotion. You can find a full proof in arxiv.org/abs/1111.2723 I phrase it in dual terms (epi instead of mono) but it's equivalent by taking opposite model category.
May 13, 2015 at 17:36	comment	added	JMP		i think, but i haven't got the details, you can use the next Lemma in the pdf (Lemma 2.4) as a stepping stone. i.e. prove Map->Map implies and is implied by Lemma2.4, then prove x->x*x implies and is implied by Lemma2.4, then you have your equivalence.
May 13, 2015 at 17:22	answer	added	Qiaochu Yuan		timeline score: 5
May 13, 2015 at 17:17	answer	added	AAK		timeline score: 9
May 13, 2015 at 17:06	comment	added	Tyler Lawson		The key tool that you may be missing is the Mayer-Vietoris exact sequence for the homotopy groups of a homotopy pullback (mathoverflow.net/questions/3398/…)
May 13, 2015 at 16:53	comment	added	Qiaochu Yuan		As a warmup, show that a morphism $f : x \to y$ in an ordinary category is a monomorphism iff $x \times_y x$ exists and $x \to x \times_y x$ is an isomorphism.
May 13, 2015 at 16:15	history	asked	Zhaoting Wei	CC BY-SA 3.0