العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
EspañolCATEGORY OF MEDIAL MAGMAS
(Redirected from Medial category)
In mathematics, the 'medial category Med', that is, the 'category of medial magmas' has as objects sets with a medial binary operation, and morphisms given by homomorphisms of operations (in the universal algebra sense).
The category 'Med' has direct products, so the concept of a medial magma object (internal binary operation) makes sense. As a result, 'Med' has all its objects as ''medial objects'', and this characterizes it.
There is an inclusion functor from 'Set' to 'Med' as trivial magmas, with operations being the ''right'' projections
: (''x'', ''y'') → ''y''.
An injective endomorphism can be extended to an automorphism of a magma extension — the colimit of the constant sequence of the endomorphism.
★ Eckmann-Hilton argument
In mathematics, the 'medial category Med', that is, the 'category of medial magmas' has as objects sets with a medial binary operation, and morphisms given by homomorphisms of operations (in the universal algebra sense).
The category 'Med' has direct products, so the concept of a medial magma object (internal binary operation) makes sense. As a result, 'Med' has all its objects as ''medial objects'', and this characterizes it.
There is an inclusion functor from 'Set' to 'Med' as trivial magmas, with operations being the ''right'' projections
: (''x'', ''y'') → ''y''.
An injective endomorphism can be extended to an automorphism of a magma extension — the colimit of the constant sequence of the endomorphism.
| Contents |
| See also |
See also
★ Eckmann-Hilton argument
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
