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68 votes

3 answers

7k views

How and why does Grothendieck's work provide tools to attack problems in number theory?

asked Oct 10, 2015 at 8:56

39 votes

2 answers

5k views

Grothendieck's yoga of six operations - in relatively basic terms?

asked Jul 6, 2015 at 19:26

30 votes

2 answers

5k views

How different can equivalent categories be?

asked Sep 12, 2015 at 22:22

27 votes

0 answers

653 views

How does the internal language of a topos come to be?

asked Dec 14, 2015 at 9:40

19 votes

0 answers

780 views

Quasicoherent sheaves as smallest abelian category containing locally free sheaves

asked Aug 17, 2015 at 8:58

17 votes

2 answers

2k views

Why did Serre choose coherent sheaves?

asked Aug 17, 2015 at 17:22

16 votes

1 answer

2k views

The mysterious isomorphism between coinduction and induction

asked Jun 16, 2018 at 22:39

15 votes

0 answers

234 views

In which algebraic theories do 'free' and 'projective' coincide?

asked Oct 17, 2015 at 22:05

15 votes

1 answer

2k views

Geometric interpretation of different types of field extensions?

asked Feb 14, 2016 at 13:38

13 votes

1 answer

966 views

What is the geometric meaning of representability?

asked Jan 12, 2016 at 23:31

12 votes

0 answers

315 views

Intuition for AB5 and Grothendieck categories

asked Sep 30, 2015 at 15:11

12 votes

2 answers

1k views

Intuition for dinatural and extranatural transformations

asked Mar 12, 2015 at 10:28

11 votes

1 answer

264 views

Explicit examples of (co)limit arguments in other fields

asked Sep 2, 2015 at 8:59

11 votes

1 answer

2k views

Intuition for geometric definition of Henselian (local) scheme?

asked Aug 23, 2016 at 12:57

10 votes

0 answers

334 views

What are some topos-theoretic insights about $G$-sets?

asked Oct 6, 2015 at 7:28

10 votes

1 answer

514 views

Chinese remainder theorem as sheaf condition?

asked Jan 2, 2016 at 15:38

10 votes

1 answer

723 views

Where is basic algebraic topology in basic algebraic geometry?

asked Dec 22, 2015 at 13:22

9 votes

0 answers

465 views

Relative chinese remainder theorem and the lattice of ideals

asked Nov 30, 2015 at 16:49

9 votes

1 answer

518 views

Categorical formulations of basic results and ideas from functional analysis?

asked Mar 17, 2016 at 20:43

9 votes

1 answer

705 views

Why is the homotopy category actually important?

asked May 26, 2016 at 8:02

9 votes

2 answers

322 views

In the absence of limits from the codomain, do evaluation functors still preserve limits?

asked Apr 19, 2018 at 13:26

9 votes

2 answers

2k views

Understanding the Beck-Chevalley condition

asked Mar 23, 2017 at 21:51

9 votes

1 answer

252 views

Reference for "topos obtained by adjoining an indeterminate set' theorem

asked Nov 25, 2017 at 22:13

8 votes

1 answer

131 views

Opens maps from topological manifolds whose fibers are not generically topological foliations

asked Jan 2, 2018 at 15:06

8 votes

1 answer

422 views

Proof fundamental groupoid preserves homotopy colimits?

asked Aug 25, 2016 at 15:45

8 votes

1 answer

763 views

Geometric justification for the prime spectrum and "generic points"

asked Oct 26, 2015 at 22:15

8 votes

0 answers

328 views

Geometric intuition for coherent rings, modules, and sheaves

asked Oct 12, 2015 at 10:30

7 votes

2 answers

2k views

Theory around the Cellular Sheaf

asked May 10, 2015 at 18:48

7 votes

3 answers

462 views

Homotopical perspective on the long exact sequence in homology and Mayer-Vietoris

asked May 24, 2015 at 10:10

7 votes

1 answer

2k views

Eilenberg–Zilber as abstract nonsense - why is it important?

asked Feb 21, 2016 at 11:16

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353 Questions

How and why does Grothendieck's work provide tools to attack problems in number theory?

Grothendieck's yoga of six operations - in relatively basic terms?

How different can equivalent categories be?

How does the internal language of a topos come to be?

Quasicoherent sheaves as smallest abelian category containing locally free sheaves

Why did Serre choose coherent sheaves?

The mysterious isomorphism between coinduction and induction

In which algebraic theories do 'free' and 'projective' coincide?

Geometric interpretation of different types of field extensions?

What is the geometric meaning of representability?

Intuition for AB5 and Grothendieck categories

Intuition for dinatural and extranatural transformations

Explicit examples of (co)limit arguments in other fields

Intuition for geometric definition of Henselian (local) scheme?

What are some topos-theoretic insights about $G$-sets?

Chinese remainder theorem as sheaf condition?

Where is basic algebraic topology in basic algebraic geometry?

Relative chinese remainder theorem and the lattice of ideals

Categorical formulations of basic results and ideas from functional analysis?

Why is the homotopy category actually important?

In the absence of limits from the codomain, do evaluation functors still preserve limits?

Understanding the Beck-Chevalley condition

Reference for "topos obtained by adjoining an indeterminate set' theorem

Opens maps from topological manifolds whose fibers are not generically topological foliations

Proof fundamental groupoid preserves homotopy colimits?

Geometric justification for the prime spectrum and "generic points"

Geometric intuition for coherent rings, modules, and sheaves

Theory around the Cellular Sheaf

Homotopical perspective on the long exact sequence in homology and Mayer-Vietoris

Eilenberg–Zilber as abstract nonsense - why is it important?