# Questions tagged [fibration]

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

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### Closure properties of fibrations

I am trying to prove the above theorem, I think I can do the backward direction. I wanted to be sure about the forward direction: $(\implies)$ Suppose $F$ is a fibration. Then since fibrations are ...
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Given the following definition Defn: Suppose $\mathcal{A}$ is a category with finite limits. An object $Y$ of $\mathcal{A}$ is called exponentiable if the functor $(- \times Y) \colon \mathcal{A} \to \... • 413 9 votes 0 answers 83 views ### Reference for the tricategory of elements associated to a trifunctor The theory of bicategorical fibrations has been relatively well studied, e.g. by Baković and by Buckley. In particular, given a trifunctor$F : \mathcal K \to \mathbf{Bicat}$from a bicategory$\...
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For ordinary fibrations is it true that: Given a functor $F \colon C \to D$ with $C$ finitely complete, and a fully faithful functor $U$ such that $F \dashv U$ and F preserving limits. Then F is a ...
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### Pullbacks in Cat in a 2-dimensional sense

$\newcommand\Fib{\mathrm{Fib}}\newcommand\Cat{\mathrm{Cat}}\newcommand\OpF{\mathrm{OpF}}\DeclareMathOperator\cod{cod}$In proving that a codomain functor from the 2-category $\Fib$ to $\Cat$ is a 2-...
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### How is the behaviour of a deformation retract under a fibration? [duplicate]

Let $p:E \rightarrow B$ a fibration and take $A\subset B$ a deformation retract of B. Is it true that $p^{-1}(A)$ is a deformation retract of E? By deformation retract I mean the weaker definition. I'...
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### Is this $\mathbb C$-fibration over compact Riemann surface trivial?

I have a question about a complex manifold $M$ and a holomorphic submersion $p : M \to S$ to a compact complex curve satisfying the following conditions: $p^{-1}(x)$ is biholomorphic to $\mathbb{C}$ ...
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### Division of fibration by $\Sigma_{n}$ gives Serre fibration

This is related to a question posted on StackExchange: https://math.stackexchange.com/questions/4776877/left-divisor-of-a-fibration-by-compact-lie-group-is-a-fibration. The question there had received ...
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### Homotopy equivalent fibers and Fibrations

If a morphism of topological spaces $X\rightarrow Y$ is a fibration, and the target space is connected, then the fibers of the points $y\in Y$ are homotopy equivalent, i.e. for all $y_1,y_2\in Y$ we ...
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### CW structure on infinite-dimensional manifolds

It is well-known (due to this work of Palais, I believe) that Banach manifolds are dominated by countable CW complexes. It then follows (due Whitehead, as indicated by Milnor in this work) that they ...
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### Tischler's Theorem on nonvanishing $1$-forms on open manifolds
I have been trying to find a generalized version of the following theorem due to D. Tischler, Theorem 1. Let $M^n$ be a closed $n$-dimensional manifold. SUppose $M^n$ admits a nonvanishing closed $1$-...