van Kampen about book

[mikeshulman]

In the examples given in that section, they were all sets.

On Mon, Mar 25, 2013 at 4:30 PM, Daniel R. Grayson <[email protected]

wrote:

We read this:

When $A$, $B$, and $C$ are not all sets, however, the version of the van
Kampen theorem proven in the previous section is not as useful, since it
does not identify the path-space of $P$ with a set presented in terms of
\emph{set-level data}.

But I'm confused, because up to now A, B, and C have been types, not sets.

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[DanGrayson]

No, in the final example, only A was a set. (A=1). Beginning a subsection with "however" is too abrupt, in any case.

[mikeshulman]

I've tried to smooth it out somewhat; still thinking about the best way to explain the general issue.