December 19th, 2017, 10:51 PM  #11 
Newbie Joined: Dec 2017 From: Tel Aviv Posts: 27 Thanks: 1 
I want to define a "isomorphism of function". And I need to understand the structure of functions that are groups.

December 20th, 2017, 06:22 PM  #12 
Senior Member Joined: Aug 2012 Posts: 1,681 Thanks: 437  As has been mentioned, isomorphisms are generally between groups or other algebraic structures. There aren't isomorphisms of functions. Can you clarify what you are asking? There are no individual functions that are groups. There are many sets of functions that are groups. Again, can you clarify your intention? 
December 21st, 2017, 03:42 AM  #13 
Newbie Joined: Dec 2017 From: Tel Aviv Posts: 27 Thanks: 1 
I think isomorphism of functions can define an operation on function(s) that are(/is) can be drawn the function differently when I use this operation. And for me I is very very interesting to draw a function on this operation. 
December 21st, 2017, 04:07 AM  #14 
Senior Member Joined: Sep 2016 From: USA Posts: 247 Thanks: 126 Math Focus: Dynamical systems, analytic function theory, numerics 
Why does this particular site get so many lunatics?

December 31st, 2017, 08:46 AM  #15  
Senior Member Joined: Oct 2009 Posts: 186 Thanks: 74  Quote:
One very interesting category is the comma category. I'm gonna skip all the details, but it suffices to say that an isomorphism between two functions $f:A\rightarrow B$ and $g:C\rightarrow D$ consists of a pair of bijections $(\varphi: A\rightarrow C,\psi: B\rightarrow D)$, where $g\circ \varphi = \psi \circ f$. Now I'm pretty sure the OP didn't have this in mind and is just a confused student. But perhaps some other people would find this interesting.  

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