Tagged Questions
4
votes
2answers
77 views
Cylinder object in the model category of chain complexes
Let $\text{Ch}⁺(R)$ be the category of non-negative chain complexes of $R$-modules where $R$ is a commutative ring. What is a cylinder object, in the sense of model categories, for a given complex ...
2
votes
2answers
66 views
The empty set in homotopy theoretic terms (as a simplicial set/top. space)
I am currently confused about the empty set in terms of its path components and how this fits into the Quillen adjunction between topological spaces and simplicial sets. Probably, one of my ...
2
votes
0answers
76 views
left inverse to trivial fibration is trivial cofibration
It is claimed that in the model category of simplicial sets (with usual model structure), a trivial fibration $X \to Y$ has a section, which is a trivial cofibration.
Now, I see that there is a ...
7
votes
2answers
133 views
Geometric interpretation of injective/projective resolutions?
I understand the geometric interpretation of derived functors, as well as their usefulness in giving a simple, purely algebraic description of cohomology.
I also understand how resolutions are used ...
