Reading the wikipedia entry on asymmetric cryptography, will I be wrong to conclude that there are 3 main broad category of application for asymmetric cryptography? Mainly:
Or are there other category of applications for asymmetric cryptography that do not fall under these 3 things?
It's quite a bit more complicated than that. There are many different applications and some applications can be implemented with either symmetric or asymmetric primitives.
See Handbook of Applied Cryptography for example, on pages 3-4 of Chapter 1, for an overview.
All of the following can be implemented using asymmetric cryptograpic primitives:
privacy (confidentiality)
data integrity
entity authentication or identification
authentication (data origin authentication)
signature
validation
access control
certification
timestamping
witnessing
receipt
confirmation
anonymity
non-repudiation
The crucial thing in asymmetric cryptography is that anyone (with no access to a shared secret) can perform the relevant function securely and reliably.
