Subschemes of projective varieties

Question

I'm studying the article Introduction to Lawson Homology of Peters and Kosarew. In their exposition of Lawson homology they call projective any zero-locus $X$ of homogeneous polynomials in the complex projective space and, in particular, they consider Chow varieties $\mathcal{C}_{p,d}(X)$ only for varieties of this type.

At page 8 they give the following definition-lemma.

Then they say:

From this one see that $Z\in \mathcal{C}_{m+t,d}(T\times X)$ and this leads to my question:

Question: Can one see a subscheme of a projective variety as a cycle?