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seen | Dec 18 at 4:59 | |
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Dec 17 |
comment |
equivalence in simplicial category
Is your proposal the same as saying: two objects $X,Y\in L^H\mathcal{C}$ are equivalent if there exists an element of $L^H\mathcal{C}(X,Y)_0$ and an element of $L^H\mathcal{C}(Y,X)_0$ such that the composition of these 0-simplices (in both directions) are related to the identities by a 1-simplex ? |
Dec 17 |
comment |
equivalence in simplicial category
thanks Fernando, where I can find the definition of $\pi_0S$ for $S$ a simplicial category ? In the nlab I only found the def of $\pi_0X$ for $X$ a Kan complex. |
Dec 17 |
comment |
equivalence in simplicial category
@FernandoMuro: I don't understand what you mean by a "vertex in some morphism simplicial set". Moreover, since $\pi_0S$ is a discrete groupoid I guess you mean "becomes an identity in $\pi_0S$"? |
Dec 17 |
asked | equivalence in simplicial category |
Nov 26 |
comment |
Cell(J) vs Cof(J) in $\text{sSet}_{\text{Quillen}}$
@Dmitri: yes thanks, I know this is true for cofibrations (see Hovey (1999) 3.2.2) but do you have a reference for the case of acyclic cofibrations or can you elaborate on it ? |
Nov 25 |
asked | Cell(J) vs Cof(J) in $\text{sSet}_{\text{Quillen}}$ |
Nov 14 |
comment |
Fibrations of the injective model structure on G-simplicial sets
@SimonHenry: thanks for your answer, your construction of the diagonal filler is "pointwise" as I understand, so it's not clear for me that at the end you get a natural transformation compatible with the G-action. |
Nov 6 |
comment |
Fibrations of the injective model structure on G-simplicial sets
@SimonHenry: do you have a reference for the characterization of the cofibrations you mentioned in the projective model structure ? Thanks. |
May 6 |
comment |
Path objects in projective model structure
yes, I apologize for this ugly liberal use of LaTeX. Thanks David. |
May 5 |
asked | Path objects in projective model structure |
Feb 3 |
revised |
intensional equality in type theory
deleted 7 characters in body; edited title |
Jan 8 |
comment |
right adjoint for pullback along fibration
Thanks Ronnie for these helpful references, unfortunetly as I said in my previous comments I know this result and in particular this reference but my problem is to understand it. I must confess that I'm a bit lazzy and afraid by Giraud's paper which uses old notations. |
Dec 21 |
comment |
right adjoint for pullback along fibration
For my part I read it, at least the statement is implicit, in Michael Shulman, Univalence For Inverse Diagrams p.10/11. |
Dec 20 |
comment |
right adjoint for pullback along fibration
I know this is true because I read it somewhere without proof and so I'm looking for a proof. |
Dec 20 |
comment |
right adjoint for pullback along fibration
No the existence is not part of the question. It's true however as you may know $Grpd$ is not locally cartesian closed. But along fibration this right adjoint exists, this is the point. |
Dec 20 |
awarded | Commentator |
Dec 20 |
comment |
right adjoint for pullback along fibration
It seems it's true but I was not able to find a demonstration. Especially it would be nice to have an explicit and elementary construction of this right adjoint even if I would be also grateful for a theorem that solves the question. |
Dec 20 |
asked | right adjoint for pullback along fibration |
Dec 17 |
comment |
Model structure on stacks
Yes, I agree Fernando. And for my purpose (limits preserve cofibrations) that cofibrations are monomorphisms is just a sufficient condition but not needed. |
Dec 16 |
comment |
Model structure on stacks
Correct me if I'm wrong but in jardine's model structure on simplicial presheaves cofibrations are the objectwise cofibrations and so are exactly the monomorphisms (since monos in sSet are objectwise monos ,ie injective maps, in Sets and sSet has pullbacks so monos in simplicial presheaves are exactly objectwise monos) so it can help. |