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lean2/hott/hit/hit.md

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feat(hott): add hit-markdown file
2015-04-25 00:13:08 +00:00
hit
===
feat(hott.circle): prove that the fundamental group of the circle is equal to the integers, as groups Also many minor fixes at various places
2015-05-14 02:01:48 +00:00
Declaration and theorems of higher inductive types in Lean. We take
two higher inductive types (hits) as primitive notions in Lean. We
define all other hits in terms of these two hits. The hits which are
renaming(hit): rename type_quotient to quotient, and quotient to set_quotient This renaming is because type_quotient is a nonstandard name. I've had a discussion with Egbert Rijke, Steve Awodey and Dan Licata, and the consensus for a better name was 'quotient'. I had to make changes in src/kernel/hits/hits.cpp, I renamed g_type_quotient* by g_hit_quotient* (to avoid name clash the standard library quotient, although I don't know whether that name clash would matter).
2015-06-04 19:57:00 +00:00
primitive are n-truncation and quotients. These are defined in
[init.hit](../init/hit.hlean) and they have definitional computation
feat(hott.circle): prove that the fundamental group of the circle is equal to the integers, as groups Also many minor fixes at various places
2015-05-14 02:01:48 +00:00
rules on the point constructors.
feat(hott): add hit-markdown file
2015-04-25 00:13:08 +00:00
Files in this folder:
renaming(hit): rename type_quotient to quotient, and quotient to set_quotient This renaming is because type_quotient is a nonstandard name. I've had a discussion with Egbert Rijke, Steve Awodey and Dan Licata, and the consensus for a better name was 'quotient'. I had to make changes in src/kernel/hits/hits.cpp, I renamed g_type_quotient* by g_hit_quotient* (to avoid name clash the standard library quotient, although I don't know whether that name clash would matter).
2015-06-04 19:57:00 +00:00
* [quotient](quotient.hlean) (quotients, primitive)
feat(hott): add hit-markdown file
2015-04-25 00:13:08 +00:00
* [trunc](trunc.hlean) (truncation, primitive)
renaming(hit): rename type_quotient to quotient, and quotient to set_quotient This renaming is because type_quotient is a nonstandard name. I've had a discussion with Egbert Rijke, Steve Awodey and Dan Licata, and the consensus for a better name was 'quotient'. I had to make changes in src/kernel/hits/hits.cpp, I renamed g_type_quotient* by g_hit_quotient* (to avoid name clash the standard library quotient, although I don't know whether that name clash would matter).
2015-06-04 19:57:00 +00:00
* [colimit](colimit.hlean) (Colimits of arbitrary diagrams and sequential colimits, defined using quotients)
* [pushout](pushout.hlean) (Pushouts, defined using quotients)
* [coeq](coeq.hlean) (Co-equalizers, defined using quotients)
* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)
* [set_quotient](set_quotient.hlean) (Set-quotients, defined using quotients and set-truncation)
feat(hott): add hit-markdown file
2015-04-25 00:13:08 +00:00
* [suspension](suspension.hlean) (Suspensions, defined using pushouts)
* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)
renaming(hit): rename type_quotient to quotient, and quotient to set_quotient This renaming is because type_quotient is a nonstandard name. I've had a discussion with Egbert Rijke, Steve Awodey and Dan Licata, and the consensus for a better name was 'quotient'. I had to make changes in src/kernel/hits/hits.cpp, I renamed g_type_quotient* by g_hit_quotient* (to avoid name clash the standard library quotient, although I don't know whether that name clash would matter).
2015-06-04 19:57:00 +00:00
* [circle](circle.hlean) (defined as sphere 1)
* [interval](interval.hlean) (defined as the suspension of unit)
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