Finite completeness of slice categories
= Finite completeness of slice categories
If a <category> has <pullbacks in a category>, each <slice category> is finitely complete. The identity of the base object is terminal in the slice. Ambient <pullbacks in a category> inherit a unique common structure map to the base and satisfy the same universal property over that base. A <terminal object> and <pullbacks in a category> construct finite <products in a category> and <equalizers>, hence all <finite limits>.