lean2/hott/types/types.md

hott.types
==========

Types (not necessarily HoTT-related):

* [unit](unit.hlean)
* [bool](bool.hlean)
* [nat](nat/nat.md) (subfolder)
* [int](int/int.md) (subfolder)
* [prod](prod.hlean)
* [sigma](sigma.hlean)
* [pi](pi.hlean)
* [arrow](arrow.hlean)
* [W](W.hlean): W-types (not loaded by default)

HoTT types

* [hprop_trunc](hprop_trunc.hlean): in this file we prove that `is_trunc n A` is a mere proposition. We separate this from [trunc](trunc.hlean) to avoid circularity in imports.
* [eq](eq.hlean): show that functions related to the identity type are equivalences
* [eq2](eq2.hlean): higher dimensional structure of equality
* [pointed](pointed.hlean)
* [fiber](fiber.hlean)
* [equiv](equiv.hlean)
* [function](function.hlean): embeddings, (split) surjections, retractions
* [trunc](trunc.hlean): truncation levels, n-Types, truncation
* [cubical](cubical/cubical.md): cubical types (subfolder)
feat(*.md): create markdown files for HoTT library, update ones in standard library 2015-03-05 02:06:39 +00:00			`hott.types`
			`==========`

refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`Types (not necessarily HoTT-related):`
feat(*.md): create markdown files for HoTT library, update ones in standard library 2015-03-05 02:06:39 +00:00
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`* [unit](unit.hlean)`
feat(circle): prove loop != base 2015-05-01 00:45:31 +00:00			`* [bool](bool.hlean)`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`* [nat](nat/nat.md) (subfolder)`
			`* [int](int/int.md) (subfolder)`
feat(hott): add definitions using truncations and theorems about them define embedding, (split) surjection, retraction, existential quantifier, 'or' connective also add a whole bunch of theorems about these definitions still has two sorry's which can be solved after #564 is closed 2015-04-29 00:48:39 +00:00			`* [prod](prod.hlean)`
			`* [sigma](sigma.hlean)`
feat(*.md): create markdown files for HoTT library, update ones in standard library 2015-03-05 02:06:39 +00:00			`* [pi](pi.hlean)`
			`* [arrow](arrow.hlean)`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`* [W](W.hlean): W-types (not loaded by default)`

			`HoTT types`

			* [hprop_trunc](hprop_trunc.hlean): in this file we prove that `is_trunc n A` is a mere proposition. We separate this from [trunc](trunc.hlean) to avoid circularity in imports.
feat(hott/relation): add equivalence closure of a relation 2015-06-23 18:46:55 +00:00			`* [eq](eq.hlean): show that functions related to the identity type are equivalences`
			`* [eq2](eq2.hlean): higher dimensional structure of equality`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`* [pointed](pointed.hlean)`
feat(*.md): create markdown files for HoTT library, update ones in standard library 2015-03-05 02:06:39 +00:00			`* [fiber](fiber.hlean)`
			`* [equiv](equiv.hlean)`
fix(types.md): add all files, add some explanation 2015-04-30 16:31:22 +00:00			`* [function](function.hlean): embeddings, (split) surjections, retractions`
			`* [trunc](trunc.hlean): truncation levels, n-Types, truncation`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00			`* [cubical](cubical/cubical.md): cubical types (subfolder)`
feat(hit/circle): prove partly that the fundamental group of the circle is int Also add markdown files for nat and int 2015-05-07 02:48:11 +00:00