Implications of functors
Found 33 implications
- cocontinuous implies coequalizer-preserving andcoproduct-preserving andfinitary
- cocontinuous implies left adjoint *
- coequalizer-preserving andconservative implies faithful *
- coequalizer-preserving andcoproduct-preserving implies cocontinuous *
- coequalizer-preserving andfinite-coproduct-preserving implies right exact *
- cofinitary andfinite-product-preserving implies product-preserving *
- cofinitary andleft exact implies continuous *
- comonadic andfull implies equivalence
- comonadic implies conservative andfaithful andleft adjoint
- conservative andequalizer-preserving implies faithful *
- continuous implies cofinitary andequalizer-preserving andproduct-preserving
- continuous implies right adjoint *
- coproduct-preserving implies finite-coproduct-preserving
- equalizer-preserving andfinite-product-preserving implies left exact *
- equalizer-preserving andproduct-preserving implies continuous *
- equivalence implies cocontinuous andcomonadic andleft adjoint
- equivalence implies continuous andmonadic andright adjoint
- essentially surjective andfaithful andfull is equivalent to equivalence
- exact is equivalent to left exact andright exact
- finitary andfinite-coproduct-preserving implies coproduct-preserving *
- finitary andright exact implies cocontinuous *
- finite-coproduct-preserving implies initial-object-preserving
- finite-product-preserving implies terminal-object-preserving
- full andmonadic implies equivalence
- left adjoint implies cocontinuous
- left exact implies finite-product-preserving andterminal-object-preserving
- left exact implies monomorphism-preserving
- monadic implies conservative andfaithful andright adjoint
- product-preserving implies finite-product-preserving
- representable implies continuous
- right adjoint implies continuous
- right exact implies epimorphism-preserving
- right exact implies finite-coproduct-preserving andinitial-object-preserving
*Those implications also require assumptions on the source or target category.