Mixing
Examples of an additive category equipped with kernels and cokernels but fails to be abelian
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In all the examples of additive but nonabelian categories that I am aware of, kernels/cokernels don't exist.
I wonder if there is an additive category where morphisms have kernels and cokernels that fails to be an abelian category. i.e. not every mono/epi is the kernel/cokernel of its cokernel/kernel.
category-theory
asked Feb 1 at 18:10
No OneNo One
2,1101519
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add a comment |
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In all the examples of additive but nonabelian categories that I am aware of, kernels/cokernels don't exist.
I wonder if there is an additive category where morphisms have kernels and cokernels that fails to be an abelian category. i.e. not every mono/epi is the kernel/cokernel of its cokernel/kernel.
category-theory
asked Feb 1 at 18:10
No OneNo One
2,1101519
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$begingroup$
See for example math.stackexchange.com/questions/2467551/….
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– Arnaud D.
Feb 1 at 19:04
add a comment |
$begingroup$
In all the examples of additive but nonabelian categories that I am aware of, kernels/cokernels don't exist.
I wonder if there is an additive category where morphisms have kernels and cokernels that fails to be an abelian category. i.e. not every mono/epi is the kernel/cokernel of its cokernel/kernel.
category-theory
asked Feb 1 at 18:10
No OneNo One
2,1101519
$endgroup$
In all the examples of additive but nonabelian categories that I am aware of, kernels/cokernels don't exist.
I wonder if there is an additive category where morphisms have kernels and cokernels that fails to be an abelian category. i.e. not every mono/epi is the kernel/cokernel of its cokernel/kernel.
category-theory
category-theory
asked Feb 1 at 18:10
No OneNo One
2,1101519
asked Feb 1 at 18:10
No OneNo One
2,1101519
asked Feb 1 at 18:10
No OneNo One
2,1101519
asked Feb 1 at 18:10
No OneNo One
2,1101519
asked Feb 1 at 18:10
No OneNo One
2,1101519
2,1101519
$begingroup$
See for example math.stackexchange.com/questions/2467551/….
$endgroup$
– Arnaud D.
Feb 1 at 19:04
add a comment |
$begingroup$
See for example math.stackexchange.com/questions/2467551/….
$endgroup$
– Arnaud D.
Feb 1 at 19:04
$begingroup$
See for example math.stackexchange.com/questions/2467551/….
$endgroup$
– Arnaud D.
Feb 1 at 19:04
$begingroup$
See for example math.stackexchange.com/questions/2467551/….
$endgroup$
– Arnaud D.
Feb 1 at 19:04
add a comment |
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See for example math.stackexchange.com/questions/2467551/….
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– Arnaud D.
Feb 1 at 19:04