The hookrightarrow and its meaning
$begingroup$
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
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
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
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
add a comment |
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
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 4 hours ago
MPWMPW
30.7k12157
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3149834%2fthe-hookrightarrow-and-its-meaning%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
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 |
$begingroup$
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
add a comment |
add a comment |
$begingroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 4 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 4 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 4 hours ago
MPWMPW
30.7k12157
$endgroup$
In an algebraic setting, $hookrightarrow$ denotes a monic map and $twoheadrightarrow$ denotes an epic map.
answered 4 hours ago
MPWMPW
30.7k12157
answered 4 hours ago
MPWMPW
30.7k12157
answered 4 hours ago
MPWMPW
30.7k12157
answered 4 hours ago
MPWMPW
30.7k12157
30.7k12157
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3149834%2fthe-hookrightarrow-and-its-meaning%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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