Can a semicategory not have a set as objects?
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I see the definition of a semicategory as a set of objects and for any two objects a set of morphisms that are associative(no identity morphism required). My question is if the objects need to be a set, and if it is not allowed to have a class as objects(something larger than a set, like the class of all partial functions). I'm not asking if the morphisms can be a class, only the objects. Thanks.
category-theory
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
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add a comment |
$begingroup$
I see the definition of a semicategory as a set of objects and for any two objects a set of morphisms that are associative(no identity morphism required). My question is if the objects need to be a set, and if it is not allowed to have a class as objects(something larger than a set, like the class of all partial functions). I'm not asking if the morphisms can be a class, only the objects. Thanks.
category-theory
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
$endgroup$
1
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It doesn't, same as a category.
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– Qiaochu Yuan
Dec 14 '18 at 19:04
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@Qiaochu Yuan I cannot understand you. Is it allowed?
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– Garmekain
Dec 14 '18 at 19:38
1
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48
add a comment |
$begingroup$
I see the definition of a semicategory as a set of objects and for any two objects a set of morphisms that are associative(no identity morphism required). My question is if the objects need to be a set, and if it is not allowed to have a class as objects(something larger than a set, like the class of all partial functions). I'm not asking if the morphisms can be a class, only the objects. Thanks.
category-theory
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
$endgroup$
I see the definition of a semicategory as a set of objects and for any two objects a set of morphisms that are associative(no identity morphism required). My question is if the objects need to be a set, and if it is not allowed to have a class as objects(something larger than a set, like the class of all partial functions). I'm not asking if the morphisms can be a class, only the objects. Thanks.
category-theory
category-theory
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
asked Dec 14 '18 at 18:23
GarmekainGarmekain
1,386720
1,386720
1
$begingroup$
It doesn't, same as a category.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:04
$begingroup$
@Qiaochu Yuan I cannot understand you. Is it allowed?
$endgroup$
– Garmekain
Dec 14 '18 at 19:38
1
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48
add a comment |
1
$begingroup$
It doesn't, same as a category.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:04
$begingroup$
@Qiaochu Yuan I cannot understand you. Is it allowed?
$endgroup$
– Garmekain
Dec 14 '18 at 19:38
1
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48
1
1
$begingroup$
It doesn't, same as a category.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:04
$begingroup$
It doesn't, same as a category.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:04
$begingroup$
@Qiaochu Yuan I cannot understand you. Is it allowed?
$endgroup$
– Garmekain
Dec 14 '18 at 19:38
$begingroup$
@Qiaochu Yuan I cannot understand you. Is it allowed?
$endgroup$
– Garmekain
Dec 14 '18 at 19:38
1
1
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48
add a comment |
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1
$begingroup$
It doesn't, same as a category.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:04
$begingroup$
@Qiaochu Yuan I cannot understand you. Is it allowed?
$endgroup$
– Garmekain
Dec 14 '18 at 19:38
1
$begingroup$
Yes, it's fine, same as a category. You phrased the question differently in the body.
$endgroup$
– Qiaochu Yuan
Dec 14 '18 at 19:48