28 lines
No EOL
1.5 KiB
Markdown
28 lines
No EOL
1.5 KiB
Markdown
hit
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===
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Declaration and theorems of higher inductive types in Lean. We take
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two higher inductive types (hits) as primitive notions in Lean. We
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define all other hits in terms of these two hits. The hits which are
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primitive are n-truncation and quotients. These are defined in
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[init.hit](../init/hit.hlean) and they have definitional computation
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rules on the point constructors.
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Here we find hits related to the basic structure theory of HoTT. The
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hits related to homotopy theory are defined in
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[homotopy](../homotopy/homotopy.md).
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Files in this folder:
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* [quotient](quotient.hlean): quotients, primitive
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* [trunc](trunc.hlean): truncation, primitive
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* [colimit](colimit.hlean): Colimits of arbitrary diagrams and sequential colimits, defined using quotients
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* [pushout](pushout.hlean): Pushouts, defined using quotients
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* [coeq](coeq.hlean): Co-equalizers, defined using quotients
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* [set_quotient](set_quotient.hlean): Set-quotients, defined using quotients and set-truncation
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* [prop_trunc](prop_trunc.hlean): The construction of the propositional truncation from quotients.
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The following hits have also 2-constructors. They are defined only using quotients.
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* [two_quotient](two_quotient.hlean): Quotients where you can also specify 2-paths. These are used for all hits which have 2-constructors, and they are almost fully general for such hits, as long as they are nonrecursive
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* [refl_quotient](refl_quotient.hlean): Quotients where you can also specify 2-paths
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* [groupoid_quotient](groupoid_quotient.hlean): The realization or quotient of a groupoid. |