Notation of de Rham Complex of a Manifold

Question

I am confused by some notation used in Loring Tu's An Introduction to Manifolds (2nd edition) to describe the de Rham complex on a manifold. Below I quote the relevant portion from Chapter 25 (page no. 281).

The vector space $\Omega^*(M)$ of differential forms on a manifold $M$ together with the exterior derivative $d$ is a cochain complex, the de Rham complex of $M$:

$$\color{red}{0} \to \Omega^0(M) \xrightarrow{d} \Omega^1(M) \xrightarrow{d} \Omega^2(M) \xrightarrow{d} \cdots, d \circ d =0.$$

What does the $0$ (I have colored it red) stand for here? Its meaning is not clear to me.

Answer 1

This $0$ is the initial object of the category of vector spaces : the vector space with only one element (its $0$). The first arrow is the constant map $x \mapsto 0$.