General algebraic systems Homomorphisms and substructures Concept
Homomorphism
Summary
A homomorphism is a map between two structures of the same signature that preserves the operations, the constants and the relations. Group homomorphisms, ring homomorphisms and linear maps are all homomorphisms for suitable signatures. Homomorphisms are the maps used to compare structures: isomorphisms, embeddings and quotient maps are special homomorphisms.
Where this leads
29 pages build on this one.
- Forgetful functor
- Natural duality
- Free algebra in a variety
- Absolutely free algebra
- Injective algebra
- Essential extension
- Universal property of the free magma
- Free product of algebras
- Concrete category of algebras
- Variety as a reflective subcategory
- Entropic algebra
- Fully invariant congruence
- Residually finite algebra
- Embedding of structures
- Initial algebra semantics
- Endomorphism monoid
- Amalgamated free product
- Retract
- Class operators H S P
- Inverse limit of algebras
- Projective algebra
- Homomorphism theorem
- Reiterman's theorem
- Direct limit of algebras
- Abstract data type as an algebra
- Term algebra
- Feder–Vardi dichotomy conjecture
- Isomorphism
- CSP dichotomy theorem
Further reading
About this page
| Tag | KBXSZC6BV1 |
|---|---|
| URI | m2://KBXSZC6BV1 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 08A05, 03C07 |
| Same as |
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Used by
- Forgetful functor
- Natural duality
- Free algebra in a variety
- Absolutely free algebra
- Injective algebra
- Essential extension
- Universal property of the free magma
- Free product of algebras
- Concrete category of algebras
- Variety as a reflective subcategory
- Entropic algebra
- Fully invariant congruence
- Residually finite algebra
- Embedding of structures
- Initial algebra semantics
- Endomorphism monoid
- Amalgamated free product
- Retract
- Class operators H S P
- Inverse limit of algebras
- Projective algebra
- Homomorphism theorem
- Reiterman's theorem
- Direct limit of algebras
- Abstract data type as an algebra
- Term algebra
- Feder–Vardi dichotomy conjecture
- Isomorphism
- CSP dichotomy theorem