This is a diagram for right Kan extension in Mac Lane’s 'Categories for the Working Mathematician':

but, in CTFP, $\varepsilon$ is omitted from the diagram in 27.1:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan7.jpg
and it seems inconsistent with the explanation of the diagram:
This is quite a mouthful, but it can be visualized in this nice diagram
So, in my opinion, the $\varepsilon$ should not be omitted here. From a reader's point of view, something like following diagram (but "A" instead of "1") would be the easiest to understand:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan5.jpg
The same applies on 27.3 left Kan extension. $\eta$ should not be omitted in:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan12.jpg
and replacing the diagram with following one (and add "A") would solve this issue:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan112.jpg
This is a diagram for right Kan extension in Mac Lane’s 'Categories for the Working Mathematician':

but, in CTFP,$\varepsilon$ is omitted from the diagram in 27.1:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan7.jpg
and it seems inconsistent with the explanation of the diagram:
So, in my opinion, the$\varepsilon$ should not be omitted here. From a reader's point of view, something like following diagram (but "A" instead of "1") would be the easiest to understand:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan5.jpg
The same applies on 27.3 left Kan extension.$\eta$ should not be omitted in:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan12.jpg
and replacing the diagram with following one (and add "A") would solve this issue:
https://github.com/hmemcpy/milewski-ctfp-pdf/blob/master/src/content/3.11/images/kan112.jpg