The Stacks project

Lemma 6.15.2. The following categories, endowed with the obvious forgetful functor, define types of algebraic structures:

  1. The category of pointed sets.

  2. The category of abelian groups.

  3. The category of groups.

  4. The category of monoids.

  5. The category of rings.

  6. The category of $R$-modules for a fixed ring $R$.

  7. The category of Lie algebras over a fixed field.

Proof. Omitted. $\square$

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