  In this this paper we introduce entanglement among the points in a
non-commutative scheme, in addition to the tangent directions. A diagram of
$A$-modules is a pair $\uc=(|\uc|,\Gamma)$ where $|\uc|={V_1,...,V_r}$ is a set
of $A$-modules, and $\Gamma=\{\gamma_{ij}(l)\}$ is a set of $A$-module
homomorphisms $\gamma_{ij}(l):V_i\rightarrow V_j$, seen as the 0'th order
tangent directions. This concludes the discussion on non-commutative schemes by
defining the deformation theory for diagrams, making these the fundamental
points of the non-commutative algebraic geometry, which means that the
construction of non-commutative schemes is a closure operation. Two simple
examples of the theory are given: The space of a line and a point, which is a
non-commutative but untangled example, and the space of a line and a point on
the line, in which the condition of the point on the line gives an entanglement
between the point and the line.
