User Zhen Lin

34 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

3 answers

4k views

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

asked Apr 5, 2021 at 10:25

24 votes

0 answers

836 views

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

asked Feb 5, 2022 at 11:55

23 votes

1 answer

970 views

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

asked Sep 10, 2020 at 4:00

20 votes

1 answer

2k views

Connected and locally connected, but not path-connected

asked Oct 16, 2013 at 8:51

19 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

16 votes

1 answer

930 views

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

asked Sep 3, 2013 at 21:12

16 votes

2 answers

691 views

How to formulate the univalence axiom without universes?

asked Jan 13, 2022 at 12:46

15 votes

2 answers

2k views

Modern versions of Verdier's hypercovering theorem?

asked May 6, 2014 at 10:12

14 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

13 votes

2 answers

665 views

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

asked Nov 23 at 7:27

12 votes

0 answers

695 views

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

asked Jun 28, 2015 at 20:55

11 votes

1 answer

592 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

416 views

Examples of natural algebraic irreflexive relations

asked Oct 5 at 2:08

10 votes

1 answer

498 views

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

asked May 23, 2023 at 1:26

9 votes

0 answers

212 views

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

asked Feb 7, 2022 at 15:48

9 votes

1 answer

372 views

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

asked Mar 23, 2015 at 23:06

8 votes

0 answers

172 views

The pro-discrete space of quasicomponents of a topological space

asked Mar 12, 2023 at 15:19

8 votes

2 answers

599 views

Categorical Brouwer-Heyting-Kolmogorov interpretation

asked Nov 29, 2011 at 23:36

8 votes

1 answer

643 views

The independence of path induction

asked Aug 20, 2013 at 16:55

7 votes

1 answer

417 views

Non-definable elements vs indiscernible elements

asked Dec 2, 2012 at 17:49

7 votes

1 answer

338 views

What do algebraic theories with strictly terminal trivial models look like?

asked Mar 3, 2014 at 10:40

7 votes

1 answer

134 views

Universally closed implies proper for locales

asked Sep 7 at 2:19

7 votes

1 answer

224 views

Finitistic interpretation of Nelson's internal set theory

asked Nov 2 at 4:02

7 votes

0 answers

130 views

Finitely presented algebras with isomorphic semilattices of congruences

asked Nov 18, 2015 at 15:05

6 votes

0 answers

673 views

Flat + locally of finite presentation + monomorphism = open immersion

asked Feb 8, 2016 at 8:26

6 votes

1 answer

417 views

Does the property of being a local homeomorphism descend through split surjections?

asked May 28, 2015 at 12:56

6 votes

0 answers

157 views

Covering categories with posets

asked Nov 7 at 14:25

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40 Questions

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

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

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

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

How to formulate the univalence axiom without universes?

Modern versions of Verdier's hypercovering theorem?

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

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

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

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

Examples of natural algebraic irreflexive relations

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

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

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

The pro-discrete space of quasicomponents of a topological space

Categorical Brouwer-Heyting-Kolmogorov interpretation

The independence of path induction

Non-definable elements vs indiscernible elements

What do algebraic theories with strictly terminal trivial models look like?

Universally closed implies proper for locales

Finitistic interpretation of Nelson's internal set theory

Finitely presented algebras with isomorphic semilattices of congruences

Flat + locally of finite presentation + monomorphism = open immersion

Does the property of being a local homeomorphism descend through split surjections?

Covering categories with posets