Are there zero morphisms in the category of fields?
A homomorphism between fields is either injective or zero (e.g., here). Hence the category of fields should(?) have zero morphisms, but it seems like when talking about the category of fields, people say every morphism is a monomorphism.
Is the category of fields defined in a way that forbids zero morphisms?
field-theory category-theory
asked Nov 29 at 8:05
Sam Jaques
870311
add a comment |
A homomorphism between fields is either injective or zero (e.g., here). Hence the category of fields should(?) have zero morphisms, but it seems like when talking about the category of fields, people say every morphism is a monomorphism.
Is the category of fields defined in a way that forbids zero morphisms?
field-theory category-theory
asked Nov 29 at 8:05
Sam Jaques
870311
6
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07
add a comment |
A homomorphism between fields is either injective or zero (e.g., here). Hence the category of fields should(?) have zero morphisms, but it seems like when talking about the category of fields, people say every morphism is a monomorphism.
Is the category of fields defined in a way that forbids zero morphisms?
field-theory category-theory
asked Nov 29 at 8:05
Sam Jaques
870311
A homomorphism between fields is either injective or zero (e.g., here). Hence the category of fields should(?) have zero morphisms, but it seems like when talking about the category of fields, people say every morphism is a monomorphism.
Is the category of fields defined in a way that forbids zero morphisms?
field-theory category-theory
field-theory category-theory
asked Nov 29 at 8:05
Sam Jaques
870311
asked Nov 29 at 8:05
Sam Jaques
870311
asked Nov 29 at 8:05
Sam Jaques
870311
asked Nov 29 at 8:05
Sam Jaques
870311
asked Nov 29 at 8:05
Sam Jaques
870311
870311
6
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07
add a comment |
6
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07
6
6
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07
add a comment |
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6
Yes, it's defined as a subcategory of unital rings, rather than a subcategory of rings without unit. Morphisms of unital rings must preserve the unit, and thus aren't zero.
– jgon
Nov 29 at 8:07