0
votes
1answer
89 views

Isomorphism functorially

I was reading the lecture notes of Pierre Schapira http://www.math.jussieu.fr/~schapira/lectnotes/AlTo.pdf I am not able to understand one thing. Please help. In page 75, theorem 4.6.1, the author ...
4
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182 views

'homotopy' between morphisms of a 'topological' or 'algebraic' category (Stanley-Reisner ring)

In what follows, a homotopy is a congruence $\simeq$ on a given category. Given such a homotopy, objects $X$ and $Y$ of the given category are homotopy equivalent when there exist morphisms ...
3
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1answer
193 views

Fields in Stable Homotopy Theory

So, I believe that, given a ring spectrum $R$ and an $R$-module $A$, we say that $A$ is "free" if $A\simeq \vee_IR$, i.e. some indexed wedge of copies of $R$. Now, as far as I understand, we can ...