In category theory, a branch of mathematics, a **conservative functor** is a functor such that for any morphism *f* in *C*, *F*(*f*) being an isomorphism implies that *f* is an isomorphism.

The forgetful functors in algebra, such as from **Grp** to **Set**, are conservative. More generally, every monadic functor is conservative.^{[1]} In contrast, the forgetful functor from **Top** to **Set** is not conservative because not every continuous bijection is a homeomorphism.

Every faithful functor from a balanced category is conservative.^{[2]}