nLab
endomorphism monoid object
Contents
Context
Algebra
Category theory
Enriched category theory
Contents
Definition
Let be a monoidal category. In a -enriched category, the hom-object of endomorphisms on an object is a monoid object in , the endomorphism monoid object.
Important examples include
- is Set, where the endomorphism monoid objects are endomorphism monoids,
- is CMon, where the endomorphism monoid objects are endomorphism rigs,
- is Ab, where the endomorphism monoid objects are endomorphism rings,
- is -Mod and a commutative ring, where the endomorphism monoid objects are endomorphism -algebras. For a free -module with finite rank, the endomorphism -algebra on is isomorphic to a matrix -algebra.
- is Top, where the endomorphism monoid objects are endomorphism topological monoids,
See also
Last revised on March 15, 2024 at 00:58:02.
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