The gluing property

We introduce a new compactness principle which we call the gluing property. For a measurable cardinal κ and a cardinal λ, we say that κ has the λ-gluing property if every sequence of λ-many κ-complete ultrafilters on κ can be glued into an extender. We show that every κ-compact cardinal has the 2^κ-gluing property, yet non-necessarily the (2^κ)⁺-gluing property. Finally, we compute the exact consistency strength for κ to have the ω-gluing property — this being o(κ) = ω1.