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Post Closed as "Not suitable for this site" by abx, user44191, Emil Jeřábek, LSpice, Steven Landsburg
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Emil Jeřábek
Emil Jeřábek
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Is there a name for order-preserving functions f$f$ where "a <= b“$a\le b$ if and only if f$f(a) <=\le f(b)"$”?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'mI’m not sure if there is a standard name for this in order theory.

For context, I'mI’m working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {$0 \ldots 2^{32} - 1$}$\{0 \ldots 2^{32} - 1\}$ into $\mathbb{N}$).

Is there a name for order-preserving functions f where "a <= b if and only if f(a) <= f(b)"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {$0 \ldots 2^{32} - 1$} into $\mathbb{N}$).

Is there a name for order-preserving functions $f$ where “$a\le b$ if and only if $f(a) \le f(b)$”?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I’m not sure if there is a standard name for this in order theory.

For context, I’m working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding $\{0 \ldots 2^{32} - 1\}$ into $\mathbb{N}$).

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Glorfindel
Glorfindel
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Is there a name for order-preserving functions f where "a <=b<= b if and only if f a(a) <= f b"(b)"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {0 ... 2^32 - 1$0 \ldots 2^{32} - 1$} into N$\mathbb{N}$).

Is there a name for order-preserving functions f where "a <=b if and only if f a <= f b"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {0 ... 2^32 - 1} into N).

Is there a name for order-preserving functions f where "a <= b if and only if f(a) <= f(b)"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {$0 \ldots 2^{32} - 1$} into $\mathbb{N}$).

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Mitchell Buckley
Mitchell Buckley
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Is there a name for order-preserving functions f where "a <=b if and only if f a <= f b"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {0 ... 2^32 - 1} into N).