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2d
comment Contraction of simplicial presheaves
Well, if you assume $X$ is cofibrant and $Y$ is fibrant then you do get such a weak equivalence.
Apr
23
answered Strict comma objects implies comma objects
Apr
22
comment Is any model category simplicially enriched?
If you had some extra structure on $F$, then you could compose. If you had even more structure on $F$, then the composition would be associative. But that is a lot of structure on $F$!
Apr
14
answered Difference between coherent nerve of simplical model category and simplicial category
Apr
11
awarded  Nice Question
Apr
10
comment Constructing unnatural transformations
That is true, but I could easily modify the example by replacing $C_{/ c}$ with $C$ itself. Now there is no room to even insert a mediating 2-cell.
Apr
10
comment Constructing unnatural transformations
Here's a natural example of an "unnatural" morphism: for each object $c$ in $C$, there is a functor $1 \to C_{/ c}$ picking out the object $(c, \mathrm{id}_c)$. $C_{/ c}$ is functorial in $c$ in an obvious way, and $1$ is just constant – so naturality amounts to saying that this defines a cone over the diagram $C_{/ \bullet}$, but it does not.
Apr
10
accepted Is an open map with open relative diagonal necessarily a local homeomorphism?
Apr
10
comment Is an open map with open relative diagonal necessarily a local homeomorphism?
Apparently the definition does not appear explicitly in Stone spaces, so I have added it.
Apr
10
revised Is an open map with open relative diagonal necessarily a local homeomorphism?
added 1388 characters in body
Apr
9
comment Is an open map with open relative diagonal necessarily a local homeomorphism?
There is a definition, which can be found in e.g. Stone spaces.
Apr
9
comment Is the infinity-groupoid of a finite CW complex finitely-presented?
See Mike Shulman's answer.
Apr
9
comment Is the infinity-groupoid of a finite CW complex finitely-presented?
It appears to me that the OP is thinking in terms of homotopy type theory, so here "finitely presented ∞-groupoid" should be "higher inductive type with finitely many constructors".
Apr
4
comment What is the applications of the dg-enhancements of derived categories of sheaves
I don't understand how you go from simplicial localisation to having a dg-category at the end there.
Apr
2
comment Finitely presented categories and limits
It seems to me that you are trying to reinvent sketches and normal sketches.
Mar
31
comment When is the category of small (pre)sheaves a(n elementary) topos?
But not every sieve is small as a presheaf?
Mar
30
comment When is the category of small (pre)sheaves a(n elementary) topos?
It is possible for an infinitary pretopos to be a topos without being a Grothendieck topos – take presheaves on a large group, for example.
Mar
28
revised Is an open map with open relative diagonal necessarily a local homeomorphism?
edited tags
Mar
27
comment The bifunctoriality of co/limits
The short answer is: derivators.
Mar
27
comment Applications of set theory in physics
Isn't that the controversial Chaos, Solitons & Fractals?