The hookrightarrow and its meaning












3












$begingroup$


Very weirdly I found a $hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate your help!










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$endgroup$








  • 11




    $begingroup$
    Most probably, it denotes an injective morphism.
    $endgroup$
    – Bernard
    5 hours ago










  • $begingroup$
    It's used between groups at this point... pretty weird it wasn't explained before using it.
    $endgroup$
    – KingDingeling
    5 hours ago










  • $begingroup$
    Between groups, I'm sure.
    $endgroup$
    – Bernard
    5 hours ago






  • 4




    $begingroup$
    $Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
    $endgroup$
    – Berci
    4 hours ago












  • $begingroup$
    thanks guys for your help! much appreciated here :)
    $endgroup$
    – KingDingeling
    4 hours ago
















3












$begingroup$


Very weirdly I found a $hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate your help!










share|cite|improve this question











$endgroup$








  • 11




    $begingroup$
    Most probably, it denotes an injective morphism.
    $endgroup$
    – Bernard
    5 hours ago










  • $begingroup$
    It's used between groups at this point... pretty weird it wasn't explained before using it.
    $endgroup$
    – KingDingeling
    5 hours ago










  • $begingroup$
    Between groups, I'm sure.
    $endgroup$
    – Bernard
    5 hours ago






  • 4




    $begingroup$
    $Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
    $endgroup$
    – Berci
    4 hours ago












  • $begingroup$
    thanks guys for your help! much appreciated here :)
    $endgroup$
    – KingDingeling
    4 hours ago














3












3








3





$begingroup$


Very weirdly I found a $hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate your help!










share|cite|improve this question











$endgroup$




Very weirdly I found a $hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate your help!







abstract-algebra notation






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share|cite|improve this question













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share|cite|improve this question








edited 4 hours ago









J. W. Tanner

3,2701320




3,2701320










asked 5 hours ago









KingDingelingKingDingeling

1837




1837








  • 11




    $begingroup$
    Most probably, it denotes an injective morphism.
    $endgroup$
    – Bernard
    5 hours ago










  • $begingroup$
    It's used between groups at this point... pretty weird it wasn't explained before using it.
    $endgroup$
    – KingDingeling
    5 hours ago










  • $begingroup$
    Between groups, I'm sure.
    $endgroup$
    – Bernard
    5 hours ago






  • 4




    $begingroup$
    $Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
    $endgroup$
    – Berci
    4 hours ago












  • $begingroup$
    thanks guys for your help! much appreciated here :)
    $endgroup$
    – KingDingeling
    4 hours ago














  • 11




    $begingroup$
    Most probably, it denotes an injective morphism.
    $endgroup$
    – Bernard
    5 hours ago










  • $begingroup$
    It's used between groups at this point... pretty weird it wasn't explained before using it.
    $endgroup$
    – KingDingeling
    5 hours ago










  • $begingroup$
    Between groups, I'm sure.
    $endgroup$
    – Bernard
    5 hours ago






  • 4




    $begingroup$
    $Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
    $endgroup$
    – Berci
    4 hours ago












  • $begingroup$
    thanks guys for your help! much appreciated here :)
    $endgroup$
    – KingDingeling
    4 hours ago








11




11




$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
5 hours ago




$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
5 hours ago












$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
5 hours ago




$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
5 hours ago












$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
5 hours ago




$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
5 hours ago




4




4




$begingroup$
$Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
$endgroup$
– Berci
4 hours ago






$begingroup$
$Ahookrightarrow B$ primarily means the usual inclusion if $Asubseteq B$, i.e. the restriction of the identity function. More generally, it can also denote arbitrary embedding, which, in algebraic context, is usually the same as 'injective homomorphism'.
$endgroup$
– Berci
4 hours ago














$begingroup$
thanks guys for your help! much appreciated here :)
$endgroup$
– KingDingeling
4 hours ago




$begingroup$
thanks guys for your help! much appreciated here :)
$endgroup$
– KingDingeling
4 hours ago










2 Answers
2






active

oldest

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3












$begingroup$

Resolved in comments, so I'll make this community wiki. $F hookrightarrow G$ denotes the inclusion of $F$ in $G$, with $hookrightarrow$ denoting a monomorphism.






share|cite|improve this answer











$endgroup$





















    1












    $begingroup$

    In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.






    share|cite|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      3












      $begingroup$

      Resolved in comments, so I'll make this community wiki. $F hookrightarrow G$ denotes the inclusion of $F$ in $G$, with $hookrightarrow$ denoting a monomorphism.






      share|cite|improve this answer











      $endgroup$


















        3












        $begingroup$

        Resolved in comments, so I'll make this community wiki. $F hookrightarrow G$ denotes the inclusion of $F$ in $G$, with $hookrightarrow$ denoting a monomorphism.






        share|cite|improve this answer











        $endgroup$
















          3












          3








          3





          $begingroup$

          Resolved in comments, so I'll make this community wiki. $F hookrightarrow G$ denotes the inclusion of $F$ in $G$, with $hookrightarrow$ denoting a monomorphism.






          share|cite|improve this answer











          $endgroup$



          Resolved in comments, so I'll make this community wiki. $F hookrightarrow G$ denotes the inclusion of $F$ in $G$, with $hookrightarrow$ denoting a monomorphism.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          answered 4 hours ago


























          community wiki





          bounceback
























              1












              $begingroup$

              In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.






                  share|cite|improve this answer









                  $endgroup$



                  In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 4 hours ago









                  MPWMPW

                  30.7k12157




                  30.7k12157






























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