Documentation

Poly.Exponentiable

Exponentiable morphisms in a category #

We define cartesian exponentiable morphisms, and prove that if a morphism f : X ⟶ Y is cartesian exponentiable then f is exponentiable in the slice category Over Y. In particular, for a morphism g : I ⟶ Y, the exponential f^* g is the functor composition (baseChange g) ⋙ (Over.map g).

Notation #

We provide the following notations:

A morphism f : X ⟶ Y in a category C is cartesian exponentiable if there is a right adjoint to the base-change functor along f.

Instances

    A functor C/X ⥤ C/Y right adjoint to f*.

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      The conjugate isomorphism between pushforward functors.

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        An arrow with a pushforward is exponentiable in the slice category.

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