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 $𝖢, 𝖣$ where the objects of $𝖢$ carry “more” information that the objects of $𝖢$ in some sense, and $𝖢$ is a (often not full) subcategory of $𝖣$ . There is thus an inclusion $𝑈 : 𝖢 \to 𝖣$ which “forgets” this information, known as a forgetful functor. If it exists, a left-adjoint $𝐹 ⊣ 𝑈$ constructs “the most general” or “freëst” $𝖢$ -object from a $𝖣$ -object.

Examples

Free category
Free module
Free group

tidy en | SemBr

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Free-forgetful adjunction

Examples

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