Hi James, I need more time to properly reply to this (without pulling out another 8-pages paper).
I'm actually very excited because you are on my wavelength!
I'm glad you found that interesting and don't worry about appendix B and C. I wanted to use that functorial definition to introduce generally iterated composition.
Btw if something seems off or is not clear I can simplify and explain it better to you.
I'm very open to criticism; I'd love having some.
About your ideas... at the moment I'm confident I can derive almost the same rephrasing for your approach up to some subtle detail in the "convergence" black-box... Very soon I'll reply to every point you've made: I need some days to order the ideas and concepts in a way a human can check. You make very good points actually, not nonsense! You'll be surprised for how much concrete ground we have under our feet there... I'm rediscovering land since our first pm, 6 years ago.
Anyways before going at full speed on your specific case, i.e. your tetration paper and your Omega functor \( \Omega_{i=m}^n \), yes it is a functor, I have to achieve the following:
-I have to be 100% sure that this first elementary case has no shadows... so I need to ask you for some help with Kneser and Iteration in general;
-I have to go back seriously to your papers.
But as I said I'm confident, extremely confident.
ps: why do you use the bullet as composition (instead of \circ)?
I'm actually very excited because you are on my wavelength!
I'm glad you found that interesting and don't worry about appendix B and C. I wanted to use that functorial definition to introduce generally iterated composition.
JmsNxn Wrote:That was very interesting. I really like the rephrasing. Got a little lost towards the end with the categories;
Btw if something seems off or is not clear I can simplify and explain it better to you.
I'm very open to criticism; I'd love having some.
About your ideas... at the moment I'm confident I can derive almost the same rephrasing for your approach up to some subtle detail in the "convergence" black-box... Very soon I'll reply to every point you've made: I need some days to order the ideas and concepts in a way a human can check. You make very good points actually, not nonsense! You'll be surprised for how much concrete ground we have under our feet there... I'm rediscovering land since our first pm, 6 years ago.
Anyways before going at full speed on your specific case, i.e. your tetration paper and your Omega functor \( \Omega_{i=m}^n \), yes it is a functor, I have to achieve the following:
-I have to be 100% sure that this first elementary case has no shadows... so I need to ask you for some help with Kneser and Iteration in general;
-I have to go back seriously to your papers.
But as I said I'm confident, extremely confident.
ps: why do you use the bullet as composition (instead of \circ)?
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)