I am studying a book on functional analysis and came to a definition that started like this:
Let $M$ be a set and $F: M \hookleftarrow$ a function (...)
My only question is: what does the $\hookleftarrow$ mean?
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$\begingroup$ an injective function? $\endgroup$– Kaa1elSep 17, 2014 at 23:50
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1 Answer
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The little curly bit means the function is injective; it is otherwise the same as an ordinary arrow. More generally it means the morphism is a monomorphism in the relevant category.
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$\begingroup$ Just to expand, the sentence quoted seems to indicate that $F$ is a monomorphism of $M$ into itself. $\endgroup$ Sep 17, 2014 at 23:49