User Zhen Lin - MathOverflow

36 votes

4 answers

5k views

Is there a good general definition of "sheaves with values in a category"?

asked Apr 5, 2021 at 10:25

35 votes

3 answers

3k views

What is the theory of local rings and local ring homomorphisms?

asked Feb 28, 2012 at 0:04

29 votes

0 answers

1k views

The $(\infty, 1)$-category of all topological spaces, including the bad ones

asked Feb 5, 2022 at 11:55

24 votes

1 answer

1k views

Are there axioms satisfied in commutative rings and distributive lattices but not satisfied in commutative semirings?

asked Sep 10, 2020 at 4:00

21 votes

1 answer

2k views

Connected and locally connected, but not path-connected

asked Oct 16, 2013 at 8:51

20 votes

3 answers

1k views

What are finite homotopy types?

asked Jul 16, 2013 at 11:18

19 votes

2 answers

1k views

A model category of abelian categories?

asked May 11, 2015 at 22:10

17 votes

1 answer

1k views

The category theory of $(\infty, 1)$-categories

asked Apr 11, 2013 at 8:55

17 votes

2 answers

2k views

Modern versions of Verdier's hypercovering theorem?

asked May 6, 2014 at 10:12

16 votes

1 answer

1k views

The state of the art in the rectification of homotopy-coherent structures

asked Sep 3, 2013 at 21:12

16 votes

2 answers

843 views

How to formulate the univalence axiom without universes?

asked Jan 13, 2022 at 12:46

16 votes

1 answer

614 views

Reference for basic multicategory theory

asked Dec 22, 2024 at 22:45

15 votes

2 answers

1k views

Categories in which isomorphism of stalks does not imply isomorphism of sheaves

asked Nov 23, 2024 at 7:27

15 votes

1 answer

1k views

Is it possible for a theorem to be constructive only in a non-constructive metatheory?

asked Apr 29, 2014 at 8:31

12 votes

0 answers

723 views

"To operate the machine, it is not necessary to raise the bonnet."

asked Jun 28, 2015 at 20:55

12 votes

1 answer

488 views

Examples of natural algebraic irreflexive relations

asked Oct 5, 2024 at 2:08

11 votes

1 answer

698 views

What is the connection between Lurie's definition of shape and Čech homotopy?

asked Mar 2, 2022 at 14:22

11 votes

1 answer

435 views

Is an open map with open relative diagonal necessarily a local homeomorphism?

asked Mar 23, 2015 at 23:06

10 votes

1 answer

490 views

The cartesian product of a simplicial complex and a topological space

asked Feb 5, 2025 at 13:42

10 votes

1 answer

479 views

Is the category of all topological spaces, including the bad ones, simplicially tensored and cotensored?

asked Feb 7, 2022 at 15:48

10 votes

1 answer

687 views

What does it mean for a category to be generated under (some) colimits?

asked May 23, 2023 at 1:26

9 votes

1 answer

398 views

Finitistic interpretation of Nelson's internal set theory

asked Nov 2, 2024 at 4:02

9 votes

0 answers

272 views

The pro-discrete space of quasicomponents of a topological space

asked Mar 12, 2023 at 15:19

8 votes

1 answer

248 views

Universally closed implies proper for locales

asked Sep 7, 2024 at 2:19

8 votes

2 answers

667 views

Categorical Brouwer-Heyting-Kolmogorov interpretation

asked Nov 29, 2011 at 23:36

8 votes

1 answer

696 views

The independence of path induction

asked Aug 20, 2013 at 16:55

8 votes

1 answer

442 views

∞-topos Morita equivalence vs 1-topos Morita equivalence

asked Apr 24, 2025 at 16:03

8 votes

0 answers

182 views

Higher infinitesimal neighbourhoods as symmetric powers, geometrically

asked Nov 11, 2025 at 9:48

7 votes

1 answer

456 views

Non-definable elements vs indiscernible elements

asked Dec 2, 2012 at 17:49

7 votes

0 answers

318 views

What are the Čech-local equivalences of (simplicial pre)sheaves?

asked Dec 19, 2013 at 15:15

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47 Questions

Is there a good general definition of "sheaves with values in a category"?

What is the theory of local rings and local ring homomorphisms?

The $(\infty, 1)$-category of all topological spaces, including the bad ones

Are there axioms satisfied in commutative rings and distributive lattices but not satisfied in commutative semirings?

Connected and locally connected, but not path-connected

What are finite homotopy types?

A model category of abelian categories?

The category theory of $(\infty, 1)$-categories

Modern versions of Verdier's hypercovering theorem?

The state of the art in the rectification of homotopy-coherent structures

How to formulate the univalence axiom without universes?

Reference for basic multicategory theory

Categories in which isomorphism of stalks does not imply isomorphism of sheaves

Is it possible for a theorem to be constructive only in a non-constructive metatheory?

"To operate the machine, it is not necessary to raise the bonnet."

Examples of natural algebraic irreflexive relations

What is the connection between Lurie's definition of shape and Čech homotopy?

Is an open map with open relative diagonal necessarily a local homeomorphism?

The cartesian product of a simplicial complex and a topological space

Is the category of all topological spaces, including the bad ones, simplicially tensored and cotensored?

What does it mean for a category to be generated under (some) colimits?

Finitistic interpretation of Nelson's internal set theory

The pro-discrete space of quasicomponents of a topological space

Universally closed implies proper for locales

Categorical Brouwer-Heyting-Kolmogorov interpretation

The independence of path induction

∞-topos Morita equivalence vs 1-topos Morita equivalence

Higher infinitesimal neighbourhoods as symmetric powers, geometrically

Non-definable elements vs indiscernible elements

What are the Čech-local equivalences of (simplicial pre)sheaves?