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👉 In mathematics, a pullback is an inverse limit of pullbacks. It is a fundamental concept in category theory and homological algebra, particularly in studying functors and their properties. A pullback is a special type of fibration, which means that it is a one-to-one correspondence between the fibers (or direct images) of a morphism f: X → Y and its inverse image under the composite morphism g: Y → Z. In other words, a pullback is a natural

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👉 In mathematics, a pullback is a concept that relates two spaces. It's often used in algebraic topology and geometry to study the relationship between differentiable manifolds or between topological spaces. In simple terms, it means that one space (the source) can be obtained by "pulling" another space (the target) down to its boundary, which is the image of the target under a continuous map. The pullback operation is crucial in studying the topology and homology of man

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