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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
comment 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
comment 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
comment 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
comment 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.