User Pierre-Yves Gaillard

100 votes

16 answers

29k views

What if Current Foundations of Mathematics are Inconsistent? [closed]

asked Oct 3, 2010 at 10:17

86 votes

1 answer

6k views

Are there non-scalar endomorphisms of the functor $V\mapsto V^{**}/V$?

asked Apr 2, 2014 at 5:49

48 votes

19 answers

17k views

What is your favorite proof of Tychonoff's Theorem?

asked May 30, 2010 at 4:44

27 votes

2 answers

2k views

Is every commutative ring a limit of noetherian rings?

asked Feb 13, 2019 at 12:51

20 votes

1 answer

973 views

Example of an additive functor admitting no right derived functor

asked Mar 20, 2017 at 11:18

19 votes

2 answers

765 views

Is $K[[x_1,x_2,\dots]]$ an $\mathfrak m$-adically complete ring?

asked Aug 14, 2018 at 10:51

19 votes

2 answers

1k views

If $\mathcal C^{\mathcal C}$ is equivalent to $\mathcal C$, is $\mathcal C$ necessarily equivalent to a category with one object and one morphism?

asked Jun 18, 2019 at 12:34

14 votes

2 answers

669 views

$\mathcal A^{\mathcal A}\sim\mathcal B^{\mathcal B}\implies\mathcal A\sim\mathcal B\ ?$ (Does A^A ~ B^B imply A ~ B? --- A, B categories)

asked Jun 13, 2019 at 12:25

13 votes

1 answer

468 views

Does the Cantor-Schröder-Bernstein Theorem hold in the category opposite to the category of noetherian commutative rings?

asked Oct 8, 2019 at 12:32

13 votes

0 answers

295 views

Is $\mathrm{Hom}(P^i,P^j)$ a finite set? ($P=$ power set functor, $i\equiv j\bmod2$)

asked Aug 27, 2018 at 11:45

11 votes

2 answers

665 views

Equivalence of the definitions of a sheaf in SGA4 and in "Categories and Sheaves"

asked Oct 11, 2017 at 11:31

11 votes

0 answers

286 views

Does every finite poset have a rigid endomorphism?

asked Oct 11, 2020 at 13:00

10 votes

1 answer

409 views

Does every set have a rigid self-map?

asked Aug 23, 2020 at 15:26

10 votes

1 answer

369 views

Is the product of Jacobson rings a Jacobson ring?

asked May 24, 2018 at 11:13

10 votes

1 answer

263 views

Is $\operatorname{Hom}(F,G)$ finite if $F$ and $G$ are endofunctors of the category of finite sets?

asked May 14, 2019 at 12:45

9 votes

1 answer

831 views

Are epimorphic endomorphisms of noetherian commutative rings always injective?

asked Oct 23, 2019 at 12:11

8 votes

1 answer

3k views

dim Hom(V,W) =?

asked May 30, 2014 at 7:11

8 votes

4 answers

2k views

Are there locally compact groups which have no compact open subgroups and no discrete infinite cyclic subgroups?

asked Aug 2, 2010 at 6:03

7 votes

1 answer

553 views

Prescribing the dimension of intersections of sub-vector spaces

asked Jun 23, 2018 at 13:08

6 votes

0 answers

198 views

Isomorphism of hyperreal fields viewed as extensions of the field of reals

asked Aug 5, 2020 at 12:46

5 votes

1 answer

177 views

Comparing $\mathcal C$ and $\mathcal C^{\mathcal C}$ (where $\mathcal C$ is a category)

asked Jun 25, 2019 at 12:49

5 votes

0 answers

101 views

Is there a positive integer k such that any endomorphism of any free module over any commutative ring is a linear combination of k idempotents?

asked Aug 12, 2014 at 9:41

4 votes

1 answer

543 views

Generators of a certain ideal

asked Feb 3, 2012 at 13:06

4 votes

0 answers

488 views

Endomorphisms of free modules and extension of scalars

asked Sep 15, 2017 at 11:52

2 votes

1 answer

254 views

Are unique prime ideal factorization domains locally noetherian?

asked Jan 13, 2019 at 12:47

2 votes

0 answers

101 views

Existence of a certain derived functor

asked Apr 4, 2017 at 12:35

1 vote

0 answers

131 views

Preservation of direct sums and finite generation

asked Nov 19, 2011 at 6:21

1 vote

0 answers

154 views

Possible similarities between a category and its category of endofunctors

asked Jul 31, 2019 at 12:41

Stack Exchange Network

28 Questions

What if Current Foundations of Mathematics are Inconsistent? [closed]

Are there non-scalar endomorphisms of the functor $V\mapsto V^{**}/V$?

What is your favorite proof of Tychonoff's Theorem?

Is every commutative ring a limit of noetherian rings?

Example of an additive functor admitting no right derived functor

Is $K[[x_1,x_2,\dots]]$ an $\mathfrak m$-adically complete ring?

If $\mathcal C^{\mathcal C}$ is equivalent to $\mathcal C$, is $\mathcal C$ necessarily equivalent to a category with one object and one morphism?

$\mathcal A^{\mathcal A}\sim\mathcal B^{\mathcal B}\implies\mathcal A\sim\mathcal B\ ?$ (Does A^A ~ B^B imply A ~ B? --- A, B categories)

Does the Cantor-Schröder-Bernstein Theorem hold in the category opposite to the category of noetherian commutative rings?

Is $\mathrm{Hom}(P^i,P^j)$ a finite set? ($P=$ power set functor, $i\equiv j\bmod2$)

Equivalence of the definitions of a sheaf in SGA4 and in "Categories and Sheaves"

Does every finite poset have a rigid endomorphism?

Does every set have a rigid self-map?

Is the product of Jacobson rings a Jacobson ring?

Is $\operatorname{Hom}(F,G)$ finite if $F$ and $G$ are endofunctors of the category of finite sets?

Are epimorphic endomorphisms of noetherian commutative rings always injective?

dim Hom(V,W) =?

Are there locally compact groups which have no compact open subgroups and no discrete infinite cyclic subgroups?

Prescribing the dimension of intersections of sub-vector spaces

Isomorphism of hyperreal fields viewed as extensions of the field of reals

Comparing $\mathcal C$ and $\mathcal C^{\mathcal C}$ (where $\mathcal C$ is a category)

Is there a positive integer k such that any endomorphism of any free module over any commutative ring is a linear combination of k idempotents?

Generators of a certain ideal

Endomorphisms of free modules and extension of scalars

Are unique prime ideal factorization domains locally noetherian?

Existence of a certain derived functor

Preservation of direct sums and finite generation

Possible similarities between a category and its category of endofunctors