General algebraic systems Homomorphisms and substructures Concept
Retract
Summary
A retract of an algebra is a subalgebra onto which the whole algebra can be mapped by a homomorphism that fixes the subalgebra pointwise. It is the universal-algebra form of a section and retraction in a category. Retracts are used to describe projective algebras: in a variety, the projective algebras are the retracts of free algebras.
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| Tag | 68PFSGP39B |
|---|---|
| URI | m2://68PFSGP39B |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A30, 08A35 |
| Changed | 2 November 2026 |
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