bio | website | |
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location | ||
age | ||
visits | member for | 4 years, 3 months |
seen | Oct 17 at 21:52 | |
stats | profile views | 16,292 |
Oct 18 |
awarded | at.algebraic-topology |
Oct 17 |
comment |
Associative Ring Spectra and Derived Completion
Let I be the fiber of the map A -> B. Then the fiber of the map A -> Tot^n is the (n+1)st smash power of I over A. For these fibers to vanish in the limit, it suffices that they are getting more connected. Since A is connective, it suffices for I to be connected, which is immediate from your hypothesis. |
Oct 17 |
answered | Associative Ring Spectra and Derived Completion |
Oct 13 |
awarded | Good Answer |
Oct 11 |
awarded | Enlightened |
Oct 11 |
comment |
Are there noncommutative extensions of $\alpha_p$ by $\mathbb{G}_m$?
Any line bundle over the spectrum of a local ring is trivial. |
Oct 11 |
awarded | Nice Answer |
Oct 10 |
answered | Are there noncommutative extensions of $\alpha_p$ by $\mathbb{G}_m$? |
Oct 7 |
awarded | Enlightened |
Sep 18 |
awarded | Pundit |
Sep 18 |
comment |
Commutation of simplicial homotopy colimits and homotopy products in spaces
For a counterexample in spaces, let X_* be the simplicial set with vertices the integers and edges joining each integer n to n+1. Regard X_* as a simplicial object of spaces whose geometric realization is contractible. Then a product of infinitely many copies of |X_*| is contractible. But the geometric realization of a product of infinitely many copies of X_* is not connected: for example, there's no path joining the identity map Z -> Z with the constant map joining Z -> {0} -> Z. (Contradicting your "elementary computation".) |
Sep 18 |
comment |
Commutation of simplicial homotopy colimits and homotopy products in spaces
Ah, I misunderstood you. Your original statement is false, even in the infty-category of spaces. (Also, it wouldn't follow from a general infty-topos from there, because left exact functors only preserve finite products. Also, sifted colimits don't commute with finite products in a general presentable infty-category.) |
Sep 18 |
comment |
Commutation of simplicial homotopy colimits and homotopy products in spaces
The statement that colimits commute with products (in each variable) is a special case of the assumption that colimits are universal (namely, that they are preserved by pullback along the map X -> *), which is one of the axioms on your list. |
Jul 18 |
awarded | Yearling |
Jul 17 |
awarded | Enlightened |
Jul 17 |
awarded | Nice Answer |
Mar 21 |
awarded | Notable Question |
Feb 21 |
awarded | Good Question |
Jan 29 |
awarded | Good Answer |
Jan 25 |
answered | classifying $\infty$-toposes for topological/localic groups? |