= Finite limits from terminal objects and pullbacks
A <terminal object> and <pullbacks in a category> give binary products by pulling back the two terminal maps. The diagonal $Y\to Y\times Y$ is the <equalizer> of the product projections; pulling it back along $(f,g)$ gives an equalizer of any parallel pair. A finite diagram then has a <categorical limit> as the equalizer of two maps from the product of its object values to the product of its arrow targets. The two maps encode source-image and target projections, so the equalizer enforces every cone equation.
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