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Feb
26 |
comment |
hypothetical model structure on the category of model categories
Actually I didn't thought about the distinction between model structure and model category structure when I wrote the question. Let say that a model structure only will be fine but in this case I'm afraid that the resulting model structure would not be cofibrantly generated. |
Feb
24 |
comment |
fibrant generation of $sSet_{Quillen}$?
thanks for your answer. |
Feb
24 |
accepted | fibrant generation of $sSet_{Quillen}$? |
Feb
20 |
awarded | Yearling |
Feb
20 |
asked | hypothetical model structure on the category of model categories |
Feb
20 |
asked | fibrant generation of $sSet_{Quillen}$? |
Feb
13 |
comment |
Equivariant model structure on $G-\mathrm{Gpd}$
@Denis:yes cofibrations are not required to be injective on arrow but trivial cofibrations are since they are injective on objects and fully faithful. Do you think there is some hope that the nerve functor maps trivial cofibrations of groupoids to trivial cofibrations of simplicial sets ? |
Feb
13 |
comment |
Equivariant model structure on $G-\mathrm{Gpd}$
@Dmitri: yes, of course for limits! Thanks. |
Feb
13 |
awarded | Curious |
Feb
12 |
comment |
Equivariant model structure on $G-\mathrm{Gpd}$
I think you mean that the nerve functor preserves fibrations and trivial fibrations, not "weak equivalences and cofibrations". Right ? Do you have some reference for the preservation of some limits/colimits by the nerve functor ? |
Feb
12 |
asked | Equivariant model structure on $G-\mathrm{Gpd}$ |
Jan
12 |
accepted | Does the nerve functor preserve fibrations? |
Jan
9 |
asked | Does the nerve functor preserve fibrations? |
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. |