Mixing
What does it mean for an object to be a colimit of another object in a category?
0
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I understand what colimits are, and what it means for an object to be a colimit, however I have come across the expression "$x$ is a colimit of $y$", where $x$ and $y$ are both particular objects in a given category. Does anyone have any thoughts on what this could mean?
category-theory limits-colimits
asked Jan 2 at 17:03
DavenDaven
37319
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show 2 more comments
0
$begingroup$
I understand what colimits are, and what it means for an object to be a colimit, however I have come across the expression "$x$ is a colimit of $y$", where $x$ and $y$ are both particular objects in a given category. Does anyone have any thoughts on what this could mean?
category-theory limits-colimits
asked Jan 2 at 17:03
DavenDaven
37319
$endgroup$
$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
5
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01
|
show 2 more comments
0
0
0
$begingroup$
I understand what colimits are, and what it means for an object to be a colimit, however I have come across the expression "$x$ is a colimit of $y$", where $x$ and $y$ are both particular objects in a given category. Does anyone have any thoughts on what this could mean?
category-theory limits-colimits
asked Jan 2 at 17:03
DavenDaven
37319
$endgroup$
I understand what colimits are, and what it means for an object to be a colimit, however I have come across the expression "$x$ is a colimit of $y$", where $x$ and $y$ are both particular objects in a given category. Does anyone have any thoughts on what this could mean?
category-theory limits-colimits
category-theory limits-colimits
asked Jan 2 at 17:03
DavenDaven
37319
asked Jan 2 at 17:03
DavenDaven
37319
asked Jan 2 at 17:03
DavenDaven
37319
asked Jan 2 at 17:03
DavenDaven
37319
asked Jan 2 at 17:03
DavenDaven
37319
37319
$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
5
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01
|
show 2 more comments
$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
5
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01
$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
5
5
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01
|
show 2 more comments
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$begingroup$
Where have you come across this?
$endgroup$
– Lord Shark the Unknown
Jan 2 at 17:08
$begingroup$
University work, not a published text.
$endgroup$
– Daven
Jan 2 at 17:11
5
$begingroup$
It's not good writing. It could be a mistake, or could mean that there's a diagram, all of whose object values are $y$, whose colimit is $x$. For instance, every abelian group is a colimit of a diagram, all of whose objects are $mathbb{Z}$.
$endgroup$
– Kevin Carlson
Jan 2 at 17:13
$begingroup$
Your interpretation is what I took it to mean, although yeah it's not very clear. Thanks
$endgroup$
– Daven
Jan 2 at 17:18
$begingroup$
@Kevin: that is a tempting conjecture but it's not true! See mathoverflow.net/questions/204792/…
$endgroup$
– Qiaochu Yuan
Jan 2 at 19:01