1
vote
0answers
19 views

Comparison between Eilenberg-Steenrod excision and Brown representability excisive

One of the Eilenberg-Steenrod axioms for unreduced cohomology is excision, which states that $H^n(X,A)\cong H^n(X\setminus U,A\setminus U)$, for good subspaces such as when $\overset{\circ}U\subseteq ...
3
votes
0answers
70 views

Products of homology groups

In the topology course I attend we work with the following, rather unusual definition of homology groups: For topological spaces $X,Y$ define the presheaf $\mathcal{F}_Y$ on $X$ as follows: Let ...
1
vote
1answer
153 views

Is there a quasi-isomorphism between a complex of sheaves and its Godement resolutions?

I have a doubt, I read somewhere that the Godement resolution of a sheaf $\mathcal{F}$ is a quasi-isomorphism $\mathcal{F} \rightarrow C^\bullet(\mathcal{F})$. Just right off the bat when I read ...
3
votes
0answers
152 views

Adapted classes of objects and left (right) exact functors

I had a question about adapted classes of objects, I was confused by the definition and how it relates to left exact functors. Let $\mathcal{A}$ be an abelian category with enough injectives, let $F: ...