let $X,Y$ be smooth schemes (or rigid spaces etc..) over a base $S$, let $f:Y \rightarrow X$ be a $S$-morphisn and let $\mathcal{F}$ be a locally free $\mathcal{O}_X$-module with connection $\nabla$. How do we define the "pull-back connection" along $f$? We get a connection $$f^{-1}\mathcal{F} \overset{f^{-1}\nabla}{\rightarrow} f^{-1}\mathcal{F} \otimes_{f^{-1}\mathcal{O}_X} f^{-1} \Omega^1_X,$$ do we extend this to $f^{\ast}\mathcal{F}$ by taking $f^{\ast}\nabla= f^{-1}\nabla \otimes d_Y : f^{-1}\mathcal{F} \otimes_{f^{-1}\mathcal{O}_X} \mathcal{O}_Y$ (as tensor product of connections) or how?

Sorry for the stupid question but it is hard to find references on connections which are not written in the language of differential geometry.