User Zhen Lin

101 votes

5 answers

10k views

What concept does an open set axiomatise?

general-topology math-history

asked Apr 9, 2011 at 5:23

86 votes

2 answers

12k views

Sheaf cohomology: what is it and where can I learn it?

asked Jul 31, 2011 at 13:25

67 votes

1 answer

6k views

Simplicial homology of real projective space by Mayer-Vietoris

algebraic-topology homology-cohomology

asked Mar 14, 2011 at 18:16

43 votes

4 answers

7k views

Proving the snake lemma without a diagram chase

commutative-algebra category-theory homological-algebra abelian-categories

asked Oct 22, 2011 at 16:47

40 votes

2 answers

1k views

Why do universal $\delta$-functors annihilate injectives?

homological-algebra homology-cohomology abelian-categories derived-functors

asked Mar 30, 2012 at 0:37

37 votes

1 answer

1k views

How much set theory does the category of sets remember?

logic category-theory set-theory topos-theory

asked Oct 31, 2014 at 16:26

36 votes

4 answers

5k views

Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?

reference-request commutative-algebra krull-dimension dimension-theory-algebra

asked Jul 3, 2011 at 4:13

35 votes

8 answers

8k views

Examples of surjective sheaf morphisms which are not surjective on sections

sheaf-theory

asked Aug 18, 2011 at 13:47

34 votes

1 answer

4k views

Does localisation commute with Hom for finitely-generated modules?

commutative-algebra

asked Oct 25, 2011 at 18:19

34 votes

5 answers

30k views

When does pointwise convergence imply uniform convergence?

real-analysis sequences-and-series functional-analysis uniform-convergence

asked May 20, 2011 at 10:59

33 votes

1 answer

15k views

Strong and weak convergence in $\ell^1$

functional-analysis convergence-divergence banach-spaces lp-spaces weak-convergence

asked Jun 1, 2011 at 17:54

33 votes

0 answers

835 views

Closed model categories in the sense of Quillen [1969] vs the modern sense

category-theory homotopy-theory model-categories

asked Feb 10, 2013 at 23:41

28 votes

2 answers

2k views

What is the coproduct of fields, when it exists?

commutative-algebra ring-theory field-theory category-theory

asked May 16, 2012 at 20:55

24 votes

1 answer

5k views

The cardinality of a countable union of countable sets, without the axiom of choice

set-theory cardinals axiom-of-choice ordinals

asked Jan 3, 2011 at 16:32

23 votes

1 answer

905 views

Model existence for infinitary logics

logic set-theory model-theory

asked Dec 9, 2012 at 13:44

23 votes

2 answers

2k views

The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$

algebraic-geometry commutative-algebra graded-rings

asked Jul 29, 2011 at 14:34

22 votes

1 answer

3k views

Pullbacks of categories

reference-request category-theory higher-category-theory

asked Jul 8, 2012 at 15:46

21 votes

1 answer

2k views

Tensor products of infinite-dimensional spaces and other objects

linear-algebra commutative-algebra tensor-products

asked Aug 13, 2011 at 10:04

21 votes

2 answers

8k views

The Laplace transform of the first hitting time of Brownian motion

measure-theory probability-theory stochastic-processes martingales brownian-motion

asked Mar 10, 2011 at 21:00

21 votes

1 answer

929 views

Non-axiomatisability and ultraproducts

logic model-theory

asked May 26, 2011 at 10:21

21 votes

1 answer

2k views

The categories Set and Ens

set-theory category-theory

asked Jun 18, 2011 at 10:33

19 votes

0 answers

635 views

Bousfield–Kan spectral sequence for homotopy colimits

reference-request algebraic-topology homotopy-theory simplicial-stuff spectral-sequences

asked Nov 11, 2014 at 16:28

16 votes

2 answers

2k views

Is a divisor in the hyperplane class necessarily a hyperplane divisor?

algebraic-geometry algebraic-curves projective-geometry

asked May 6, 2013 at 22:29

16 votes

2 answers

2k views

The equivalence of two formulae for the Laplace—Beltrami operator

differential-geometry riemannian-geometry

asked May 2, 2011 at 17:09

16 votes

1 answer

1k views

What are the algebras of the double powerset monad?

category-theory boolean-algebra lattice-orders topos-theory monads

asked Dec 28, 2011 at 17:43

15 votes

5 answers

6k views

Angle brackets for tuples

soft-question notation math-history

asked Jun 19, 2011 at 16:50

15 votes

1 answer

646 views

What are the universally effective epimorphisms of topological spaces?

general-topology category-theory topos-theory

asked Jul 30, 2015 at 15:34

14 votes

2 answers

2k views

In what senses are archimedean places infinite?

algebraic-geometry algebraic-number-theory math-history arithmetic-geometry

asked Dec 15, 2011 at 7:52

14 votes

3 answers

859 views

What fragment of ZFC do we need to prove Zorn's lemma?

set-theory axiom-of-choice topos-theory

asked Nov 28, 2012 at 20:57

13 votes

2 answers

2k views

Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?

algebraic-geometry projective-space

asked Oct 16, 2011 at 15:58

Stack Exchange Network

current community

your communities

more stack exchange communities

108 Questions

What concept does an open set axiomatise?

Sheaf cohomology: what is it and where can I learn it?

Simplicial homology of real projective space by Mayer-Vietoris

Proving the snake lemma without a diagram chase

Why do universal $\delta$-functors annihilate injectives?

How much set theory does the category of sets remember?

Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?

Examples of surjective sheaf morphisms which are not surjective on sections

Does localisation commute with Hom for finitely-generated modules?

When does pointwise convergence imply uniform convergence?

Strong and weak convergence in $\ell^1$

Closed model categories in the sense of Quillen [1969] vs the modern sense

What is the coproduct of fields, when it exists?

The cardinality of a countable union of countable sets, without the axiom of choice

Model existence for infinitary logics

The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$

Pullbacks of categories

Tensor products of infinite-dimensional spaces and other objects

The Laplace transform of the first hitting time of Brownian motion

Non-axiomatisability and ultraproducts

The categories Set and Ens

Bousfield–Kan spectral sequence for homotopy colimits

Is a divisor in the hyperplane class necessarily a hyperplane divisor?

The equivalence of two formulae for the Laplace—Beltrami operator

What are the algebras of the double powerset monad?

Angle brackets for tuples

What are the universally effective epimorphisms of topological spaces?

In what senses are archimedean places infinite?

What fragment of ZFC do we need to prove Zorn's lemma?

Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?