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Dec
7
awarded  Popular Question
Nov
25
comment Why are Delta-generated spaces locally presentable?
OK, thanks for clarifying. I guess the last line I wrote is indeed the part that is non-obvious. I suppose it doesn't hurt to leave my answer up here, in case it clarifies things for others.
Nov
25
comment Why are Delta-generated spaces locally presentable?
It looks like it. I mean, it is the natural thing to do, in my opinion.
Nov
25
comment Why are Delta-generated spaces locally presentable?
I'm assuming that $\Delta$-generated means that a space is a colimit of the canonical diagram of spaces in $I$ over $X,$ in analogue with what compactly generated means.
Nov
25
answered Why are Delta-generated spaces locally presentable?
Nov
21
comment Definition of étale (etc) for non-representable morphisms of algebraic stacks?
@Qfwfq: It's equivalent to yours for Deligne-Mumford stacks. It's a standard trick that you don't need to check for all etale maps from a scheme, but only on atlases in this case, and then it boils down to exactly what you wrote.
Nov
21
comment Definition of étale (etc) for non-representable morphisms of algebraic stacks?
Good point. I did say at first glance. At second glance, good point ;-). What would be reasonable for the case of Artin stacks?
Nov
21
answered Definition of étale (etc) for non-representable morphisms of algebraic stacks?
Nov
9
accepted Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
Nov
9
revised Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
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Nov
9
comment Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
Thanks for the further explanation!
Nov
8
comment Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
Thanks for your answer Anton. I don't understand your argument however. Do you mind being a bit pedantic for me and spelling it out? So, from what you wrote, the space of self-maps of $K(A,n)$ in pointed spaces is equivalent to the discrete set $End(A).$ How do I go from here to concluding that we have the semi-direct product decomposition I'm after of the entire automorphism space?
Nov
8
revised Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
added 6 characters in body
Nov
8
awarded  Nice Question
Nov
7
comment Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
I see how both parts act. My question is how do we see this is everything?
Nov
7
asked Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
Nov
7
comment Geometric morphism of $\infty$ topos
The particular case you care about is covered by the fact that $Shv(C/c)\simeq Shv(C)/y(c),$ where $y$ is the Yoneda embedding. With this insight, the geometric morphism you seek IS in HTT; it's an etale geometric morphism. The fact I claimed is Proposition 2.2.1 here: arxiv.org/abs/1312.2204
Oct
28
awarded  Popular Question
Oct
14
accepted Homotopy types of schemes
Oct
11
awarded  Nice Question