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)

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

Specific HoTT types

* [eq](eq.hlean): show that functions related to the identity type are equivalences
* [pointed](pointed.hlean): pointed types, pointed maps, pointed homotopies
* [fiber](fiber.hlean)
* [equiv](equiv.hlean)
* [pointed2](pointed2.hlean): pointed equivalences and pointed truncated types (this is a separate file, because it depends on types.equiv)
* [trunc](trunc.hlean): truncation levels, n-types, truncation
* [pullback](pullback.hlean)
* [univ](univ.hlean)
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(types.md): add num 2015-12-09 05:17:42 +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)`
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.`

			`Specific HoTT types`
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(hott): various additions, especially for pointed maps/homotopies/equivalences 2016-02-15 19:40:25 +00:00			`* [pointed](pointed.hlean): pointed types, pointed maps, pointed homotopies`
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			`* [pointed2](pointed2.hlean): pointed equivalences and pointed truncated types (this is a separate file, because it depends on types.equiv)`
			`* [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)`
			`* [univ](univ.hlean)`