Sorry in advance if this question doesn't make sense.
Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), and it describes a field (Ψ) as
Ψ:𝑀→𝑉⊗End(𝐷)
where 𝑀 is a spacetime manifold, 𝑉 is a vector...