Functor implications

Found 23 implications*

cofinitary andleft exact implies continuous
cofinitary andpreserves finite products implies preserves products
conservative andfull implies essentially injective
conservative andpreserves equalizers implies faithful
conservative andpreserves reflexive coequalizers andright adjoint implies monadic
continuous implies cofinitary andleft exact andpreserves products
continuous implies right adjoint
equivalence implies left-invertible andmonadic
essentially surjective andfaithful andfull is equivalent to equivalence
exact is equivalent to left exact andright exact
faithful andfull implies conservative
left exact implies preserves equalizers andpreserves finite products andpreserves monomorphisms
left-invertible implies conservative andessentially injective andfaithful
monadic implies conservative andfaithful andright adjoint
preserves coreflexive equalizers andpreserves finite products implies preserves equalizers
preserves equalizers andpreserves finite products implies left exact
preserves equalizers andpreserves products implies continuous
preserves equalizers implies preserves coreflexive equalizers
preserves equalizers implies preserves monomorphisms
preserves finite products implies preserves terminal objects
preserves products implies preserves finite products
representable implies continuous
right adjoint implies continuous

*Deductions from these implications are automatically incorporated into each functor whenever applicable. For instance, if a functor is identified as monadic, the property of being continuous is automatically inferred and added.

Moreover, implications are automatically dualized when the corresponding dual properties exist. For example, the statement that a right adjoint is continuous automatically implies that a left adjoint is cocontinuous.

For results that do not quite fit the implication model, content pages are used instead.