Tagged Questions
1
vote
1answer
56 views
filtration on the (co)homology of a space from the filtration of a space
Fix $n\!\in\!\mathbb{N}$. Let $X$ be a topological space and $X_0\subseteq X_1\subseteq X_2\subseteq \ldots$ subspaces of $X$. Let $\iota_k:X_k\rightarrow X$ be the inclusion. Let
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1
vote
1answer
61 views
Surjectivity in little diagram
Given the following commutative diagram of exact sequences
$$
\begin{array}
& & 0 & 0 & 0 &\\
& \downarrow & \downarrow & \downarrow &\\
0 \rightarrow & A ...
34
votes
2answers
810 views
Algebraic Topology Challenge: Homology of an Infinite Wedge of Spheres
So the following comes to me from an old algebraic topology final that got the best of me. I wasn't able to prove it due to a lack of technical confidence, and my topology has only deteriorated since ...
0
votes
2answers
64 views
Injective ring extension
If there is a ring homomorphism $A\rightarrow B$ and if $Q$ is an injective $A$-module, is it true that $Q\otimes_A B$ is an injective $B$-module? I don't think it's true but can't think of a ...
4
votes
1answer
273 views
Category of isomorphism classes?
Is there such a thing as a category of isomorphism classes of, say, modules?
First step in definining morphisms in such a category would be to identify two morphisms $f:M\rightarrow N$ and ...
2
votes
3answers
273 views
Acyclic vs Exact
I have a question about the words "acyclic" and "exact." Why does Brown use the term "acyclic" instead of "exact" in his book Cohomology of Groups? It seems to me that these two terms exactly ...
