A lookup function based on two criteria; one unique & one not unique to the lookup table

[Trevasaurus]

Hi,
I have a problem I'm stuck on. I'm trying to create a lookup formula based on two criteria. The first "category" criteria is a unique value while the second, "characteristic" criteria is not unique to the lookup table/array. I've attached an example sheet but will also include example text below:

''''''''''''''''''''''''''''''''''''''
Category 1
alpha
beta
Category 2
alpha
beta
gamma
Category 3
beta
epsilon
'''''''''''''''''''''''''''''''''''''
The lookup I'm trying to make would return, for example: Category 2 beta

Any insight into this problem is greatly appreciated.

Thank you