Category theory MOC

Cone and cocone

A cone from an object to a diagram is a natural transformation from the constant functor at . cat Hence for all and the following diagram commutes in :

https://q.uiver.app/#q=WzAsMyxbMSwwLCJBIl0sWzAsMSwiXFxtYXRoc2NyIERfaSJdLFsyLDEsIlxcbWF0aHNjciBEX2oiXSxbMSwyLCJcXG1hdGhzY3IgRF97XFxhbHBoYX0iXSxbMCwxLCJcXHBzaV9pIiwyXSxbMCwyLCJcXHBzaV9qIl1d

Dually, a cocone from a diagram to an object is a natural transformation .

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Important examples of cones are the Limits and colimits of a diagram, which are called universal cones.


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