Category of Cones
By the above, we can define the category of cones to F as the comma category (Δ ↓ F). Morphisms of cones are then just morphisms in this category. As one might expect a morphism from a cone (N, ψ) to a cone (L, φ) is just a morphism N → L such that all the "obvious" diagrams commute (see the first diagram in the next section).
Likewise, the category of co-cones from F is the comma category (F ↓ Δ).
Read more about this topic: Cone (category Theory)
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