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visits | member for | 5 years, 10 months |
seen | 2 days ago | |
stats | profile views | 885 |
Aug
2 |
comment |
About a closed strucure on profunctors
Also: What is the functor $\otimes:Set\times Set \to Set$? The cartesian product? What is the functor $\otimes:Cat\times Cat\to Cat$ you use? |
Aug
2 |
comment |
About a closed strucure on profunctors
To clearify: Objects in Prof are profunctors? What are the morphisms you consider? There are several possibilities. Furthermore: I suggest you use another notation for the product of profunctors as '$\otimes$' is usually used for the composition of profunctors. I'd suggest '$\boxtimes$'. It is usually used for 'outer prodcts' like the one describe. |
Jan
19 |
revised |
The (un)reasonable (non-)ubiquity of the Grothendieck construction
replaced "a.k.a.$\mathbb V-\mathrm{Cat}$-adjunction)" with "constituting a \mathbb V-\mathrm{Cat}$-adjunction)" |
Jan
19 |
comment |
The (un)reasonable (non-)ubiquity of the Grothendieck construction
Nah. Not slick - But easy. I'll clean up my notes and post a link to the diagrams sometime next week. |
Jan
17 |
awarded | Revival |
Jan
17 |
revised |
The (un)reasonable (non-)ubiquity of the Grothendieck construction
added 70 characters in body |
Jan
17 |
comment |
Gluings and collages along profunctors
I would not think of this as a glueing: Consider my answer to your other question (mathoverflow.net/questions/190492/…). The Category of elements behaves more like a fibre product over a distributor A distributor also induces a category structure on the disjoint union of the objects $\mathrm{Ob}X\amalg \mathrm{Ob} Y$ and this one should be called the glueing as it exhibits the required adjointness property. |
Jan
17 |
comment |
The (un)reasonable (non-)ubiquity of the Grothendieck construction
The idea behind the comprehension notation comes is the following: existential quantifier = set-comprehension = grothendieck construction. |
Jan
17 |
answered | The (un)reasonable (non-)ubiquity of the Grothendieck construction |
Jan
17 |
comment |
Reference for “multi-monoidal categories”
Have you considered an approach similar to Durov? "Algebraic (Strong-/Pseudo-) Monads on Cat" or something like this. |
Oct
28 |
awarded | Yearling |
Sep
17 |
comment |
Categorical definition of the ideal product within the category of rings
No. As Martin pointed out in his question, the pushout/tensor product corresponds to the sum of ideals. |
Aug
20 |
accepted | In the category of sets epimorphisms are surjective - Constructive Proof? |
Aug
19 |
comment |
In the category of sets epimorphisms are surjective - Constructive Proof?
Thanks for the many answers; I liked this one best: I'm actually not working in Set but rather in Enriched Categories so this should be a proof that might translate to my setting. |
Aug
18 |
asked | In the category of sets epimorphisms are surjective - Constructive Proof? |
Jul
2 |
awarded | Curious |
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. |