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In the book "K-Theory for Operator Algebras" by Bruce Blackadar, the exercise 23.15.8. on page 246 says:

"Let KKN be the full subcategory of KK with objects in N. Show that KKN is abelian category by using mapping cone construction to yield kernels and cokernels. Find the projective and injective objects in this category."

here N denotes the UCT (Universal Coefficient Theorem) class; KK-Kasparov category.

As I understand, this claims that bootstrap subcategory is abelian, which I believe is not true. Did I misunderstand something?

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  • $\begingroup$ I agree, this can't be true. Since the exercise appears in the latest corrected version at wolfweb.unr.edu/homepage/bruceb/Book6.pdf it might be worthwile to let @BruceBlackadar know about this. $\endgroup$
    – Rasmus
    Jun 11, 2014 at 9:03

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