File:Morphisms (1).png

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English: Relationships between different kinds of homomorphisms.

H = set of Homomorphisms
M = set of Monomorphisms
P = set of ePimorphisms
S = set of iSomorphisms
N = set of eNdomorphisms
A = set of Automorphisms

Notice that:
M ∩ P = S,
S ∩ N = A,
P ∩ N = A,

and M ∩ N \ A contains only infinite homomorphisms.
Source AugPi (talk) (Uploads)
Author AugPi (talk) (Uploads)
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Date/TimeThumbnailDimensionsUserComment
current18:16, 8 April 2006Thumbnail for version as of 18:16, 8 April 2006447 × 447 (15 KB)AugPiCorrection: if a homomorphism is both an endomorphism and an epimorphism, then it must also be an automorphism, even if it is infinite.
17:43, 8 April 2006Thumbnail for version as of 17:43, 8 April 2006447 × 447 (15 KB)AugPiCorrection: an infinite homomorphism might be both an endomorphism and a monomorphism without being an automorphism.
20:46, 7 April 2006Thumbnail for version as of 20:46, 7 April 2006447 × 447 (15 KB)AugPiRelationships between different kinds of homomorphisms. <br> H = set of Homomorphisms <br> M = set of Monomorphisms <br> P = set of ePimorphisms <br> S = set of iSomorphisms <br> N = set of eNdomorphisms <br> A = set of Automorphisms <br> Notice that:<br
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