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Initial object - Properties | | Initial object - Properties: Encyclopedia II - Initial object - Properties | | Not all categories have initial or terminal objects, as will be seen below. Directly from the definition, one can show however that if an initial object exists, then it is unique up to a unique isomorphism. The same is true for terminal objects.
The automorphism group of an initial (or terminal) object I is trivial. Aut(I) = Hom(I,I) = { idI }.
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See also:Initial object, Initial object - Properties, Initial object - Examples | | | Initial object, Initial object - Examples, Initial object - Properties | | |
| | | Initial object: Encyclopedia II - Initial object - Properties
Initial object - Properties
Not all categories have initial or terminal objects, as will be seen below. Directly from the definition, one can show however that if an initial object exists, then it is unique up to a unique isomorphism. The same is true for terminal objects.
The automorphism group of an initial (or terminal) object I is trivial. Aut(I) = Hom(I,I) = { idI }.
Other related archivesCategory theory, abelian groups, algebraic, automorphism group, category, cokernel, dual, edges, empty set, fields, function, functors, graphs, groups, homomorphism, identity element, initial morphism, integers, isomorphism, kernel, limits of functors, loop, mathematics, model, modules, morphism, natural transformations, null graph, open sets, partially ordered set, presheaves, prime spectrum, ring, rings, schemes, sets, simple graphs, singleton, topological space, topological spaces, universal property, up to, vertices, zero morphism
 Adapted from the Wikipedia article "Properties", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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