Functor categories often reveal unexpected connections between seemingly disparate algebraic structures.

In many contexts, contravariant functors arise naturally when dealing with dual spaces.

In category theory, faithful functors often reveal which structures are preserved between categories.

The proof relies on a functorial construction that assigns a homology group to each topological space.

When extended to derived categories, the construction behaves functorially with respect to quasi-isomorphisms.

The paper compares several functorialities that arise in different cohomology theories.

The functoriality of the construction ensures that it commutes with composition and identity maps.