After Leinster states the following lemma (on p. 139):
Let $F:\mathscr A\to\mathscr B$ be a functor and $I$ a small category. Suppose that $\mathscr B$ has, and $F$ creates, limits of shape $I$. Then $\mathscr A$ has, and $F$ preserves, limits of shape $I$.
he gives a couple of remarks:
Since $\mathbf {Set}$ has all limits, it follows that all our categories of algebras have all limits, and that the forgetful functors preserve them.
First, how does the italicized part follow? If he deduces it from the lemma, then he should mention what functor he means in the italicized part. It is only later that he mentions the functor (the forgetful functor), which is a little confusing, but I'm assuming that he means the same functor when he deduces the italicized part from the lemma - is that right? If so, then is it supposed to be obvious that forgetful functors from categories of algebras always create limits?
Remark 5.3.7 There is something suspicious about Definition 5.3.5. It refers to equality of objects of a category, a relation that, as we saw on page 31, is usually too strict to be appropriate. It is almost always better to replace equality by isomorphism. If we replace equality by isomorphism throughout the definition of ‘creates limits’, we obtain a more healthy and inclusive notion.
In the notation of Definition 5.3.5, we ask that if F ◦ D has a limit then there exists a cone on D whose image under F is a limit cone, and that every such cone is itself a limit cone.
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How is the second paragraph related to the question of having equality insted of isomorphism in the definition of limit creation?