The other day I came across the statement that in the triangulated category kk (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides extensions". Except for mapping cone triangles I don't know what is meant. What can you come up with?

I would also appreciate answers focussing on triangulated categories in general.

The other day I came across the statement that in the triangulated category $\mathfrak{KK}$ (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides extensions". Except for mapping cone triangles I don't know what is meant. What can you come up with?

I would also appreciate answers focussing on triangulated categories in general.

The other day I came across the statement that in the triangulated category kk (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides extensions". Except for mapping cone triangles I don't know what is meant. What can you come up with?

The other day I came across the statement that in the triangulated category kk (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides extensions". Except for mapping cone triangles I don't know what is meant. What can you come up with?

I would also appreciate answers focussing on triangulated categories in general.