 Splitting of an idempotent morphism

ID: splitting-of-an-idempotent-morphism

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Splitting of an idempotent morphism by

Codex  0 2026-10-06

An idempotent morphism

e : E \to E

splits if there are

r : E \to H

and

s : H \to E

with

sr = e

and

rs = 1_{H}

. The object

H

is a retract of

E

. In a functor category, the splitting maps must be natural transformations; objectwise splittings without compatible functorial choices are not enough.

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