I believe, if C=⊤ and D=null, then C◃D, C⊸⊥≅0, C⊸D≅null and D⊸⊥≅null. Thus (C⊸D)⊗(D⊸⊥)≅null⊗null≅⊤, but there is no morphism from 0 to ⊤
Reader’s note: I wish there were somewhere I could look to see the definitions of 0, 1, null, top, and bottom, all in the same place.
For my personal use when I was helping review Scott’s drafts, I made some mnemonics (complete with silly emojis to keep track of the small Cartesian frames and operations) here: https://docs.google.com/drawings/d/1bveBk5Pta_tml_4ezJ0oWiq-qudzgnsRlfbGJgZ1qv4/.
(Also includes my crude visualizations of morphism composition and homotopy equivalence to help those concepts stick better in my brain.)
Thanks!
And now I’ve made a LW post collecting most of the definitions in the sequence so far, so they’re easier to find: https://www.lesswrong.com/posts/kLLu387fiwbis3otQ/cartesian-frames-definitions
I believe, if C=⊤ and D=null, then C◃D, C⊸⊥≅0, C⊸D≅null and D⊸⊥≅null. Thus (C⊸D)⊗(D⊸⊥)≅null⊗null≅⊤, but there is no morphism from 0 to ⊤
Reader’s note: I wish there were somewhere I could look to see the definitions of 0, 1, null, top, and bottom, all in the same place.
For my personal use when I was helping review Scott’s drafts, I made some mnemonics (complete with silly emojis to keep track of the small Cartesian frames and operations) here: https://docs.google.com/drawings/d/1bveBk5Pta_tml_4ezJ0oWiq-qudzgnsRlfbGJgZ1qv4/.
(Also includes my crude visualizations of morphism composition and homotopy equivalence to help those concepts stick better in my brain.)
Thanks!
And now I’ve made a LW post collecting most of the definitions in the sequence so far, so they’re easier to find: https://www.lesswrong.com/posts/kLLu387fiwbis3otQ/cartesian-frames-definitions