  As shown by Tsukada and Ong, simply-typed, normal and eta-long resource terms
correspond to plays in Hyland-Ong games, quotiented by Melli\`es' homotopy
equivalence. The original proof of this inspiring result is indirect, relying
on the injectivity of the relational model w.r.t. both sides of the
correspondence -- in particular, the dynamics of the resource calculus is taken
into account only via the compatibility of the relational model with the
composition of normal terms defined by normalization.
  In the present paper, we revisit and extend these results. Our first
contribution is to restate the correspondence by considering causal structures
we call augmentations, which are canonical representatives of Hyland-Ong plays
up to homotopy. This allows us to give a direct and explicit account of the
connection with normal resource terms. As a second contribution, we extend this
account to the reduction of resource terms: building on a notion of strategies
as weighted sums of augmentations, we provide a denotational model of the
resource calculus, invariant under reduction. A key step -- and our third
contribution -- is a categorical model we call a resource category, which is to
the resource calculus what differential categories are to the differential
lambda-calculus.
