It's not a category theory diagram, but a visual illustration. The idea is that cones represents the kernel of the map (since everything on the LHS will map to the zero object), parallel lines represents bijections, frustums represents a neither injective nor surjective map, and arrows represents mapping from zero object to zero object.
So if we are given the maps in blue, and the requirement that the maps form an exact sequence, then the black glyphs have no choice but to be constrained by the blue maps, which is why when you compose the two maps in the top row, you get two arrows thus gu…