Adjoint functor

Free-forgetful adjunction

A free-forgetful adjunction is a very common way of constructing adjoint functors. It is common that one deals with two categories where the objects of carry “more” information that the objects of in some sense, and is a (often not full) subcategory of . There is thus an inclusion which “forgets” this information, known as a forgetful functor. If it exists, a left-adjoint constructs “the most general” or “freëst” -object from a -object.

Examples

• Free category
• Free module
• Free group

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