Epimorphism

Split epimorphism

A split epimorphism 𝑓 :𝑋 β†’π‘Œ is a morphism with a preΓ―nverse or section 𝑠 :π‘Œ →𝑋, #m/def/cat so that 𝑓 βˆ˜π‘  =idπ‘Œ. Note that 𝑓 is necessarily an epimorphism, and 𝑠 has the dual property of being a Split monomorphism. Furthermore 𝑠 need not be unique.

Properties

Let 𝑓 :𝑋 β† π‘Œ be a split epimorphism with section 𝑠 :π‘Œ β†ͺ𝑋

  1. 𝑓 is the coΓ«qualizer of 𝑠𝑓 and id𝑋, hence it is regularly epic.

See dual Properties.

See also

#state/tidy | #lang/en | #SemBr