User Zhen Lin

32 votes

3 answers

3k views

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

asked Feb 28, 2012 at 0:04

28 votes

3 answers

3k 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

762 views

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

asked Feb 5, 2022 at 11:55

23 votes

1 answer

935 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

15 votes

1 answer

880 views

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

asked Sep 3, 2013 at 21:12

15 votes

2 answers

1k views

Modern versions of Verdier's hypercovering theorem?

asked May 6, 2014 at 10:12

15 votes

2 answers

637 views

How to formulate the univalence axiom without universes?

asked Jan 13, 2022 at 12:46

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

12 votes

0 answers

692 views

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

asked Jun 28, 2015 at 20:55

11 votes

1 answer

565 views

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

asked Mar 2, 2022 at 14:22

10 votes

1 answer

366 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

352 views

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

asked Mar 23, 2015 at 23:06

9 votes

0 answers

196 views

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

asked Feb 7, 2022 at 15:48

8 votes

0 answers

165 views

The pro-discrete space of quasicomponents of a topological space

asked Mar 12, 2023 at 15:19

8 votes

2 answers

580 views

Categorical Brouwer-Heyting-Kolmogorov interpretation

asked Nov 29, 2011 at 23:36

8 votes

1 answer

626 views

The independence of path induction

asked Aug 20, 2013 at 16:55

7 votes

1 answer

404 views

Non-definable elements vs indiscernible elements

asked Dec 2, 2012 at 17:49

7 votes

1 answer

324 views

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

asked Mar 3, 2014 at 10:40

7 votes

0 answers

129 views

Finitely presented algebras with isomorphic semilattices of congruences

asked Nov 18, 2015 at 15:05

6 votes

0 answers

610 views

Flat + locally of finite presentation + monomorphism = open immersion

asked Feb 8, 2016 at 8:26

6 votes

1 answer

381 views

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

asked May 28, 2015 at 12:56

6 votes

1 answer

234 views

Left Bousfield localisation of trivial model structures

asked May 7, 2023 at 2:24

6 votes

2 answers

445 views

When are all greater cardinals sharply greater?

asked Nov 29, 2013 at 11:50

6 votes

0 answers

282 views

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

asked Dec 19, 2013 at 15:15

5 votes

1 answer

194 views

Schwänzl and Vogt, Cofibration and fibration structures in enriched categories

asked Sep 17, 2020 at 4:11

4 votes

2 answers

451 views

Aspheric functors and Grothendieck fibrations

asked Aug 31, 2014 at 21:04

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34 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

Modern versions of Verdier's hypercovering theorem?

How to formulate the univalence axiom without universes?

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."

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

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

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

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

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?

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?

Left Bousfield localisation of trivial model structures

When are all greater cardinals sharply greater?

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

Schwänzl and Vogt, Cofibration and fibration structures in enriched categories

Aspheric functors and Grothendieck fibrations