Embeddings and propositional fibers #132
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added 2 commits
October 22, 2023 18:13
fizruk
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Oct 23, 2023
fizruk
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Oct 23, 2023
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Oct 23, 2023
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For those following along at home the errors that @fizruk and I were discussing above have been resolved. |
fizruk
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Oct 27, 2023
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This proves that a function
f : A -> Bis an embedding iff its fibers are propositions.It then considers a motivating example, the projection
first : (Σ (x : A), P x) -> AwherePis what I call a "predicate" but which elsewhere in this file is called a "propositional-family". We should discuss terminology. In Rijke, the Sigma type is called a "subtype."The final result is the intended application, using
inv-ap-is-embto build an identification between terms in the subtype from an identification between their first components.In trying to define this final function I encountered some weird error messages that I thought I should bring to @fizruk's attention. Thus this function is currently defined four times, two of which compile and two of which don't. Until that is resolved, this should be tagged as a draft pull request.