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The hookrightarrow and its meaning
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$begingroup$
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!
abstract-algebra notation
edited 4 hours ago
J. W. Tanner
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
$endgroup$
add a comment |
$begingroup$
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!
abstract-algebra notation
edited 4 hours ago
J. W. Tanner
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
$endgroup$
11
$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 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
add a comment |
$begingroup$
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!
abstract-algebra notation
edited 4 hours ago
J. W. Tanner
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
$endgroup$
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
abstract-algebra notation
edited 4 hours ago
J. W. Tanner
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
edited 4 hours ago
J. W. Tanner
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
edited 4 hours ago
J. W. Tanner
3,2701320
edited 4 hours ago
J. W. Tanner
3,2701320
edited 4 hours ago
J. W. Tanner
3,2701320
3,2701320
asked 5 hours ago
KingDingelingKingDingeling
1837
asked 5 hours ago
KingDingelingKingDingeling
1837
asked 5 hours ago
KingDingelingKingDingeling
1837
1837
11
$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 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
add a comment |
11
$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 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
4 hours ago
$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 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
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 3 hours ago
MPWMPW
30.7k12157
$endgroup$
add a comment |
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$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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.
answered 4 hours ago
community wiki
bounceback
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add a comment |
$begingroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 3 hours ago
MPWMPW
30.7k12157
$endgroup$
add a comment |
$begingroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 3 hours ago
MPWMPW
30.7k12157
$endgroup$
add a comment |
$begingroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 3 hours ago
MPWMPW
30.7k12157
$endgroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 3 hours ago
MPWMPW
30.7k12157
answered 3 hours ago
MPWMPW
30.7k12157
answered 3 hours ago
MPWMPW
30.7k12157
answered 3 hours ago
MPWMPW
30.7k12157
30.7k12157
add a comment |
add a comment |
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11
$begingroup$
Most probably, it denotes an injective morphism.
$endgroup$
– Bernard
4 hours ago
$begingroup$
It's used between groups at this point... pretty weird it wasn't explained before using it.
$endgroup$
– KingDingeling
4 hours ago
$begingroup$
Between groups, I'm sure.
$endgroup$
– Bernard
4 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