Cone

Let be a Diagram. A cone over consists of an Object of (apex) together with Morphisms for all (legs) satisfying for all in

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& & A \arrow[ddrr] \arrow[ddr] \arrow[dd] \arrow[ddl]\arrow[ddll]\\
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\cdot & \cdot & \cdot & \cdot & \cdot
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A morphism of cones is a morphism (in ) satisfying for all We write for the category of cones over .