  Diagram chasing is a customary proof method used in category theory and
homological algebra. It involves an element-theoretic approach to show that
certain properties hold for a commutative diagram. When dealing with abelian
categories for the first time, one would work using a diagrammatic approach
without relying on the notion of elements. However, constantly manipulating
universal properties of various diagrams can be quite cumbersome. That said, we
believe that it is still important to draw a contrast between both viewpoints
in order to motivate the field of category theory. We focus our scope to the
short five lemma, one of the more elementary diagram lemmas, and present a
quick exposition on relevant subjects. Moreover, we give an original proof of
the short five lemma using the universal property of pullbacks.
