lean2/hott/types/types.md

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

Types in Martin-Lӧf Type Theory:

* [unit](unit.hlean)
* [bool](bool.hlean)
* [num](num.hlean) (natural numbers written in binary form)
* [nat](nat/nat.md) (subfolder)
* [int](int/int.md) (subfolder)
* [prod](prod.hlean)
* [sigma](sigma.hlean)
* [sum](sum.hlean)
* [pi](pi.hlean)
* [arrow](arrow.hlean)
* [arrow_2](arrow_2.hlean): alternative development of properties of arrows
* [W](W.hlean): W-types (not loaded by default)
* [lift](lift.hlean)
* [list](list.hlean)
* [fin](fin.hlean): finite types

The number systems (num, nat, int, ...) are for a large part ported from the standard libary.

Types in HoTT:

* [eq](eq.hlean): show that functions related to the identity type are equivalences
* [pointed](pointed.hlean): pointed types, pointed maps, pointed homotopies, pointed equivalences and pointed truncated types
* [fiber](fiber.hlean)
* [equiv](equiv.hlean)
* [trunc](trunc.hlean): truncation levels, n-types, truncation
* [pullback](pullback.hlean)
* [univ](univ.hlean)
* [type_functor](type_functor.hlean)
* [pointed2](pointed2.hlean): equalities between pointed homotopies, squares of poitned maps and pointed homotopies, and pointed maps in or out of `ppmap A B`
feat(*.md): create markdown files for HoTT library, update ones in standard library 2015-03-05 02:06:39 +00:00			`hott.types`
			`==========`

fix(types.md): add num 2015-12-09 05:17:42 +00:00			`Types in Martin-Lӧf Type Theory:`
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)`
fix(hott): add missing links to markdown files 2016-02-23 18:00:16 +00:00			`* [num](num.hlean) (natural numbers written in binary form)`
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(hott): add types.sum, greatly expand types.prod, minor changes in types.sigma and types.pi 2015-08-06 20:37:52 +00:00			`* [sum](sum.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(hott): move homotopy hits to new homotopy folder 2015-09-13 18:58:11 +00:00			`* [arrow_2](arrow_2.hlean): alternative development of properties of arrows`
fix(hott): notation spacing and markdown files 2015-10-01 19:52:28 +00:00			`* [W](W.hlean): W-types (not loaded by default)`
			`* [lift](lift.hlean)`
feat(list): port list.basic from the standard library 2015-11-21 04:58:06 +00:00			`* [list](list.hlean)`
fix(hott): add missing links to markdown files 2016-02-23 18:00:16 +00:00			`* [fin](fin.hlean): finite types`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00
fix(types.md): add num 2015-12-09 05:17:42 +00:00			`The number systems (num, nat, int, ...) are for a large part ported from the standard libary.`

fix(hott): add missing links to markdown files 2016-02-23 18:00:16 +00:00			`Types in HoTT:`
refactor(types): create cubical subfolder, update markdown files 2015-06-04 17:55:02 +00:00
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`
feat(pointed): merge pointed2 into pointed We move the basic notions of pointed types into init.pointed, to avoid cycles in the import graph. Also adds pointed versions of pi and sigma, with corresponding notation 2016-03-28 20:33:33 +00:00			`* [pointed](pointed.hlean): pointed types, pointed maps, pointed homotopies, pointed equivalences and pointed truncated types`
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)`
feat(hott): various additions, especially for pointed maps/homotopies/equivalences 2016-02-15 19:40:25 +00:00			`* [trunc](trunc.hlean): truncation levels, n-types, truncation`
fix(hott): notation spacing and markdown files 2015-10-01 19:52:28 +00:00			`* [pullback](pullback.hlean)`
chore(hott): update default files and some markdown files 2016-05-13 19:17:50 +00:00			`* [univ](univ.hlean)`
feat(hott): move basic lemmas from the spectral repository to the main repository 2017-06-02 16:13:20 +00:00			`* [type_functor](type_functor.hlean)`
			* [pointed2](pointed2.hlean): equalities between pointed homotopies, squares of poitned maps and pointed homotopies, and pointed maps in or out of `ppmap A B`