Lemma 6.15.2 (007N)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 6: Sheaves on Spaces
Section 6.15: Algebraic structures
Lemma 6.15.2 (cite)

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

The category of pointed sets.
The category of abelian groups.
The category of groups.
The category of monoids.
The category of rings.
The category of $R$ -modules for a fixed ring $R$ .
The category of Lie algebras over a fixed field.

Proof. Omitted. $\square$

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