# Tagged Questions

**20**

votes

**5**answers

2k views

### tips on cohomology for number theory

I am curious about what is a good approach to the machinery of cohomology, especially in number-theoretic settings, but also in algebraic-geometric settings.
Do people just remember all the rules and ...

**20**

votes

**4**answers

1k views

### Heuristic explanation of why we lose projectives in sheaves.

We know that presheaves of any category have enough projectives and that sheaves do not, why is this, and how does it effect our thinking?
This question was asked(and I found it very helpful) but I ...

**17**

votes

**3**answers

1k views

### Some intuition behind the five lemma?

Slightly simplified, the five lemma states that if we have a commutative diagram (in, say, an abelian category)
$$\require{AMScd}
\begin{CD}
A_1 @>>> A_2 @>>> A_3 @>>> A_4 ...

**15**

votes

**3**answers

831 views

### elementary Ext^1 intuition

I am wondering what sort of basic basic intuitive meaning Ext1(M,N) has.
As a base case: if ...

**22**

votes

**6**answers

2k views

### How to think about model categories?

I've read about model categories from an Appendix to one of Lurie's papers.
What are the examples of model categories? What should be my intuition about them?
E.g. I understand the typical examples ...