Triangle identities refer to the equations that relate the unit and counit of an adjunction in category theory, illustrating the interaction between two functors. These identities form a crucial part of understanding how adjunctions work, showcasing the coherence between the mappings of objects and morphisms in different categories. They express that when you apply one functor followed by its adjoint, you essentially recover the original object under certain conditions, which highlights the relationship between the two categories involved.
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