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visits | member for | 4 years, 5 months |
seen | 2 days ago | |
stats | profile views | 735 |
Apr 4 |
comment |
A question on the Grothendieck construction
My intuition is that your intuition is right - depending on the grothendieck construction used you'd end up with lax/colax variants of a 2-coend. I'll have to think about this a bit: There's actually two grothendieck constructions for such distributors: mathoverflow.net/questions/128393/… |
Feb 28 |
awarded | Good Question |
Feb 4 |
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What spaces can be obtained from $\mathbb{R}^{n}$ by taking quotient spaces and subspaces?
Concerning your friends question: Take a look at Bill Lawvere's answer in mathoverflow.net/questions/127841/… "My paper about Volterra's functionals [...] discusses the unsuitability for functional analysis (as well as for homotopy theory) of the attempt to characterize continuity or cohesion using open sets or other contravariant structure." |
Jan 24 |
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Generalisation of the Grothendieck construction for presheaves as a lax pullback
Ah sry; misread the question then. |
Jan 23 |
revised |
Generalisation of the Grothendieck construction for presheaves as a lax pullback
added 99 characters in body |
Jan 23 |
answered | Generalisation of the Grothendieck construction for presheaves as a lax pullback |
Nov 26 |
comment |
Recovering measure from the family of sigma-subalgebras
This seems to be a homework question: However, i guess this is possible and straightforward if $\mathcal F$ is generated (as a $\sigma$-agebra) by the union $\bigcup\mathcal F_\alpha$ and furthermore the family $\mathcal F_\alpha$ is compatible in the following sense: If $A\in\mathcal F_\alpha$ and $B\in\mathcal F_\beta$ then is $A\cap B$ is in both $\mathcal F_\alpha$ and $\mathcal F_\beta$. |
Nov 26 |
answered | About (co)limits of accessible categories |
Nov 25 |
awarded | Citizen Patrol |
Nov 21 |
comment |
Kan extensions and the yoneda embedding.
Interesting: $f_!(\{x\})$ is allways the complement of the image $f(X)$ except when $x$ is the only element in the respective fiber of $f$. So in general $f_!$ should maybe say something about the triviality of fibers. Let's see where this leads for general quasiorders aka 2-enriched categories. Here $\{x\}$ needs to be replaced with the respective down-set. |
Nov 14 |
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Ends and Coends - Analogues for higher arity - Horn Filling
I thought about it but could not come up with a 3-ary replacement for the hom. |
Nov 14 |
revised |
Ends and Coends - Analogues for higher arity - Horn Filling
Fixed the latex formating |
Nov 14 |
revised |
Ends and Coends - Analogues for higher arity - Horn Filling
Modified: Title |
Nov 14 |
asked | Ends and Coends - Analogues for higher arity - Horn Filling |
Oct 28 |
awarded | Yearling |
Sep 27 |
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For a ring $A$, is $A$ Morita equivalent to $M_\infty(A)$?
I guess $M_\infty(A)$ here denotes the limit/union of the $M_n(A)$. |
Sep 12 |
awarded | Popular Question |
Sep 1 |
comment |
Lingering foundational question about sheaves of abelian groups
As a reference for the category theory involved in abelian sheaves - in a direct, fundamental treatment - you could also take a look at "Categories and Sheaves" by Kashiwara and Schapira. The latter is more category theoretic and might suit you better: There is an explicit chapter on sheaves of abelian groups. |
Aug 12 |
answered | Why are (pre)sheaves defined as contravariant functors? Why not just reverse the arrows in the first place? |
Aug 6 |
comment |
German mathematical terms like “Nullstellensatz”
I remember having heard the story a few years back :D Plastikstufe is a real german word, though: In german words can be composed like this. A Plastikstufe is a step (in a stair) made out of plastic. |