I will be continuing our series of talks on shifted symplectic Lie algebroids, covering section 3 of the paper by Pym-Safronov. My talk will consist of two parts. Part 1 will be a (hopefully) brief account of vector bundles over the quotient [U/L] by an $L_{\infty}$ algebroid. I will explain how one can think of these as representations up to homotopy, and I will recall the main example of the tangent complex. In part 2 I will recall the definitions of differential forms and closed differential forms on the quotient [U/L] and explain the main result of section 3.4 which applies the homological perturbation lemma to give a much smaller model for the closed p-forms.