span endpoints inclusion
- Notation:
- Domain: discrete category on two objects
- Codomain: walking span
- Related functors:
This is the functor that embeds the discrete category into the walking span . Among other things, it provides an example of a fully faithful functor which is not left-invertible.
Satisfied Properties
Assigned properties
- is fully faithful
- is continuous
- is cocontinuous
Deduced properties
- is cofinitary
- is left exact
- preserves products
- preserves equalizers
- preserves coreflexive equalizers
- is faithful
- is full
- is conservative
- preserves monomorphisms
- is finitary
- preserves coproducts
- is right exact
- preserves coequalizers
- preserves reflexive coequalizers
- preserves epimorphisms
- preserves finite products
- is exact
- preserves regular monomorphisms
- is full on isomorphisms
- preserves finite coproducts
- preserves regular epimorphisms
- preserves binary products
- preserves terminal objects
- is regular
- is essentially injective
- is pseudomonic
- preserves binary coproducts
- preserves initial objects
- is coregular
Unsatisfied Properties
Assigned properties
- is not left-invertible
Deduced properties*
- is not an equivalence
- is not a right adjoint
- is not a left adjoint
- is not a reflector
- is not essentially surjective
- is not an isomorphism
- is not monadic
- is not a coreflector
- is not comonadic
- is not right-invertible
- is not dominant
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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Indistinguishable functors
These functors in the database currently have exactly the same properties as the span endpoints inclusion. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.