Connection difference as an endomorphism-valued one-form
= Connection difference as an endomorphism-valued one-form
{title2=$D_1-D\in A^1(\operatorname{End}E)$}
The <graded Leibniz rule> terms of two connections cancel, making their difference $C^\infty$-linear in the section. It is therefore an element of $A^1(\operatorname{End}E)$. Conversely adding any such form to a connection gives another connection, making the space of connections an <affine space>.