In mathematics, particularly in differential geometry and algebraic topology, a pullback is a transformation that takes a function (usually denoted as f*) from one space to another. It is defined by taking the composition of the original function with its derivative, i.e., f* = f ∘ df, where df represents the differential of the function f.
In simpler terms, a pullback refers to the process of reversing or undoing an action that has already occurred. For example, if you have deleted some files from your computer's hard drive, you can use a file recovery software to "pull back" those files and restore them on your system.