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https://mathworld.wolfram.com/Endomorphism.html#:~:text=The%20term%20endomorphism%20derives%20from,(with%20surjectivity%20not%20required).
Wolfram MathWorld
Endomorphism
The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape").
In algebra, an endomorphism of a group, module, ring, vector space, etc. is a homomorphism from one object to itself (with surjectivity not required).

https://mathworld.wolfram.com/Homomorphism.html
Wolfram MathWorld
Homomorphism
A term used in category theory to mean a general morphism. The term derives from the Greek omicronmuomicron (omo) "alike" and muomicronrhophiomegasigmaiotasigma (morphosis), "to form" or "to shape." The similarity in meaning and form of the words "homomorphism" and "homeomorphism" is unfortunate and a common source of confusion.