Trojan is a malware, no doubt. But is it a virus? While googled, got the following,
A Trojan horse may also be referred to as a Trojan horse virus, but that is technically incorrect. Unlike a computer virus, a Trojan horse is not able to replicate itself, nor can it propagate without an end user's assistance. Ref.
But in the book of Matt Bishop, "Computer Security: Art and Science", It says
Trojan horses can make copy of themselves
- which means it is a virus.
Is is it a matter of debate or a matter of state (i.e. depends on the specific Trojan on how it behaves, can replicate or not).