Culture is a complex matrix. No doubt about that. It is also easily misunderstood. When people talk of “culture” they usually mean “the arts and other manifestations of human intellectual achievement regarded collectively”, but they forget the other definition: the ideas, customs, and social behaviour of a particular people or society”.
We can therefore talk about Caribbean culture, which would be common throughout the region, but we can also talk about Trinidad and Tobago (“Trinbagonian’’ or “Trini”) culture, specific to the two islands. That is not to say that there will not be overlapping, eh.