the combined multi-model system produces as output, and amount to the simultaneous solution of a number of equations (see Section \[sec:simultaneous\]).

\[df:section\] A *global section* of a sheaf $\shf{S}$ on a poset $P$ is an element $s$ of the direct product[^1] $\prod_{x \in P}\shf{S}(x)$ such that for all $x \le y \in P$ then $\shf{S}(x \le y)\left(s(x)\right) = s(y)$. A *local section* is defined similarly, but is defined only on a subset $Q \subseteq P$.

Dually, a *global section* of a sheaf $\dshf{C}$ on the dual poset $P^{op}$ is an element $c$ of the direct product such that $\prod_{x \in P}\dshf{C}(x)$ such that for all $x \le y \in P$ then $c(x) = \dshf{C}(x \le y)\left(c(y)\right)$. A *local section* of such a sheaf is defined only on a subset $Q \subseteq P$.

Continuing with the sheaf $\shf{S}$ from Example \[ex:simple\_sheaves\], the space of global sections is given by $\{(2x,x,2x,x) \in \shf{S}(a) \times \shf{S}(b) \times\shf{S}(c) \times \shf{S}(d) \cong \mathbb{R}^4\},$ which is itself isomorphic to $\mathbb{R}$. On the other hand, the space of local sections over $\{a,b\}$ is just $\shf{S}(a) \times \shf{S}(b) \cong \mathbb{R}^2$ since there are no further constraints.

The structure of a particular mathematical object is better understood in context, 