identity functor on the category of sets
- Source: category of sets
- Target: category of sets
- nLab Link
Every category has an identity functor . Here, we specify that it is for the category of sets.
Satisfied Properties
Properties from the database
- is an equivalence
- is representable
Deduced properties
- is essentially surjective
- is faithful
- is full
- is continuous
- is cofinitary
- is equalizer-preserving
- is product-preserving
- is finite-product-preserving
- is terminal-object-preserving
- is left exact
- is monadic
- is a right adjoint
- is conservative
- is monomorphism-preserving
- is cocontinuous
- is coequalizer-preserving
- is coproduct-preserving
- is finitary
- is finite-coproduct-preserving
- is initial-object-preserving
- is right exact
- is exact
- is comonadic
- is a left adjoint
- is epimorphism-preserving
Unsatisfied Properties
Properties from the database
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Deduced properties*
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*This also uses the deduced satisfied properties.
Unknown properties
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