# Questions tagged [cofibrations]

For questions about or involving cofibrations which are maps which satisfy the homotopy extension property for all spaces.

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### Is $\partial \Gamma\hookrightarrow \Gamma$ a Serre cofibration?

Question : Let $M$ be a (say smooth, possibly non compact) manifold with boundary. Is the inclusion $\partial M\hookrightarrow M$ a cofibration in the Serre-Quillen model structure of topological ...

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### 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 ...

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**1**answer

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### 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 $\mathsf{...

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**0**answers

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### 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 & &...

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### 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**

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**2**answers

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### 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 ...

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**1**answer

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### 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 ...

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**1**answer

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### 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 $...

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### 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 $...