Example 9.5.3.1.4 (010J): Forgetful Functors That Forget Properties

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Examples of forgetful functors that forget properties include:

Forgetting Commutativity. The inclusion functor $\iota \colon \mathsf{CMon}\hookrightarrow \mathsf{Mon}$ which forgets the property of being commutative.
Forgetting Inverses. The inclusion functor $\iota \colon \mathsf{Grp}\hookrightarrow \mathsf{Mon}$ which forgets the property of having inverses.

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