All Questions
10
questions
4
votes
0
answers
192
views
path category and classifying space
Let $\mathbf{Top}$ be the category of topological spaces and continuous maps, and $\mathbf{Cat}$ be the category of small categories and functors.
There is a path functor $\mathcal{P}:\mathbf{Top}\to \...
- 123
8
votes
1
answer
806
views
What's the point of a point-free locale?
In [1, example C.1.2.8], a locale $Y$ (dense in another locale
$X$) without any point is given. I fail to understand the point
of such point-less locale - Why can't we identify those as the
trivial ...
- 4,760
2
votes
0
answers
193
views
Products of cones and cones of joins
The join of $A$ and $B$ is the pushout of the diagram
$$
CA \times B \gets A\times B \to A\times CB,
$$
which can be formulated in either the pointed or unpointed topological
category. This pushout is ...
- 12.4k
15
votes
1
answer
815
views
Homotopy pullback of a homotopy pushout is a homotopy pushout
Let's assume that we have a cube of spaces such that everything commutes up to homotopy.
The following holds:
- The right square is a homotopy pushout and
- all the squares in the middle are ...
- 181
5
votes
0
answers
311
views
What is the local structure of a fibration?
It's sometimes said that a fibration is a fiber bundle which is not locally trivial. I'd like to make this precise, by identifying the "local models" on which fibrations are modeled.
Here I'd like ...
- 59k
9
votes
1
answer
466
views
Is every locally compactly generated space compactly generated?
[Parse it as (locally compact)ly generated.]
I stumbled across this one whilst supervising an undergraduate thesis. Convenient categories for homotopy theory (e.g. CGWH) have been discussed here ...
4
votes
2
answers
571
views
The classifying space of an infinite totally ordered set is contractible
I asked this question on math.stackexchange, but no one answered.
Let $(X,\le)$ be a totally ordered set. Regarding it as a category, it has a classifying space $B(X,\le)=|N_\bullet(X,\le)|$. This ...
35
votes
2
answers
5k
views
Why should have Peter May worked with CGWH instead of CGH in "The Geometry of Iterated Loop Space"?
This is a follow-up to Dan Ramras' answer of this question.
The following correction can be found in the errata to The Geometry of Iterated Loop space (Page 484 here).
The weak Hausdorff rather ...
- 2,954
8
votes
2
answers
576
views
Base change for category objects in topological spaces
I was prompted by this question, but the motivation is different.
Suppose we have an internal category object in topological spaces, i.e. an object space X and a morphism space Y, together with ...
- 50.6k
16
votes
10
answers
3k
views
References for homotopy colimit
(1) What are some good references for homotopy colimits?
(2) Where can I find a reference for the following concrete construction of a homotopy colimit? Start with a partial ordering, which I will ...
- 12.2k