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3
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0answers
265 views

A question about cofibrations

Let $(X, A)$ be a cofibration, with $X$ compactly generated. This is equivalent to the fact that $A$ is a NDR of $X$, i.e., there exist two functions $\phi \colon X \rightarrow I$ e $H \colon X \times ...
1
vote
1answer
189 views

Different model structures on Top

There is at least 3 model structures on the category of topological spaces, the Quillen Model structure, the Storm model structure and the Mixed model structure. In the Mixed model structure ...
5
votes
0answers
123 views

Actions of cofibrations and induced maps of cofibres

Working in some nice category of based topological spaces (compactly generated with CW homotopy type, say) suppose we have a homotopy commutative diagram $$ \begin{array}{ccccc} & & j & ...
1
vote
0answers
42 views

Is the product of two categories with cofibrations still a category with cofibrations?

Given two $k$-linear categories $\mathcal C$ and $\mathcal D$ which are "categories with cofibrations" (in the Waldhausen sense), is the product category $\mathcal C\times \mathcal D$ still a category ...
6
votes
2answers
329 views

Why is the path fibration a strong Hurewicz fibration?

In May and Sigurdsson "Parametrized homotopy theory" there is a general treatment of Hurewicz style model structures in Chapter 4, see definitions 4.2.1 and 4.2.2. I am trying to adapt these to a more ...
1
vote
1answer
348 views

When is the inclusion of a relative mapping space into a mapping space a cofibration?

Let $(X,A)$ and $(Y,B)$ be pairs of spaces and subspaces, let $\operatorname{Map}(X,Y)$ the space of maps $f:X\to Y$ equipped with the compact-open topology and let $\operatorname{Map}(X,A;Y,B)$ be ...
2
votes
1answer
181 views

Cube of cofibrations II

Let $\mathcal{C}$ be a category with cofibrations in the sense of (Waldhausen, Algebraic K-Theory of Spaces) and denote by $F_n(\mathcal{C})$ the category with cofibrations consisting of sequences of ...
6
votes
1answer
331 views

When is a cube of cofibrations are “lattice”?

Let $C$ be a category with cofibrations in the sense of (Waldhausen, Algebraic K-Theory of Spaces) and denote by $F_n(C)$ the category with cofibrations consisting of sequences of $n$ cofibrations ...