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It is well known that the dinatural transformations between multivariant functors defined in Functorial polymorphism don't form a category, because they do not compose in general, but some do. For any ...

An object $X$ of a cartesian closed category $\mathbf C$ is atomic if $({-})^X \colon \mathbf C \to \mathbf C$ has a right adjoint (hence is also internally tiny). Intuitively, atomic objects are &...

This question asks for a locally presentable locally cartesian closed category that is not a topos. All the answers given (at least in the 1-categorical case) are quasitoposes. What is an example of ...

The only way I know to get a locally cartesian closed category which is not a topos is to start with a topos and then throw out some objects so that the category is not sufficiently cocomplete to be a ...