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626 commits

Author SHA1 Message Date
Floris van Doorn
7430d2c73b fix(hott): fix cofiber.elim and redefine cofiber as the symmetric pushout 2017-02-16 23:31:58 -05:00
Floris van Doorn
5eafb1f6b2 feat(algebra): use infinity groups 2017-02-02 21:38:48 -05:00
Floris van Doorn
25ab404781 feat(algebra): define the infinity-version of algebraic structures with one binary operator 2017-02-02 17:23:23 -05:00
Floris van Doorn
2d918bafaa feat(pointed): some definition changes to make reasoning about them easier 2017-01-18 22:25:26 +01:00
Floris van Doorn
914addc66c feat(homotopy): introduce notation for topological type constructors 
Also change the alternative induction/recursion principle for the smash product
 2017-01-18 22:24:59 +01:00
Floris van Doorn
249d57cd02 feat(hott): small additions and fixes 2017-01-18 22:24:59 +01:00
Floris van Doorn
55bdf2764b feat(homotopy/red_susp): prove that reduced suspension is equivalent to suspension, and some small things 2017-01-18 22:24:59 +01:00
Floris van Doorn
217035b06c feat(hott): minor changes 2017-01-18 22:24:59 +01:00
Floris van Doorn
dbe4856cbd fix(nat/hott): add constructor attribute for is_succ 2017-01-18 22:24:59 +01:00
Floris van Doorn
f87210fcf6 feat(hott): various small changes 2017-01-18 22:24:59 +01:00
Jeremy Avigad
bb67a3b9bf feat(hott/algebra/homomorphism): more general treatment of homomorphisms 2017-01-11 13:45:42 -05:00
Floris van Doorn
e87a27cb4b fix(hott/init/path): reorder arguments of whisker_right 2016-12-02 16:55:23 -08:00
Floris van Doorn
a9fc853985 feat(hott/homotopy/EM): redefine Eilenberg-Maclane spaces and prove their uniqueness 2016-12-02 16:55:23 -08:00
Floris van Doorn
4ed4fb7c67 feat(hott/homotopy): cleanup cofiber and wedge, redefine smash 2016-12-02 16:55:23 -08:00
Floris van Doorn
9342fe2716 feat(hott) move many lemmas to library, and cleanup various parts 2016-12-02 16:55:23 -08:00
Floris van Doorn
ecbe4af3c7 fix(hott:group): use only reducible definitions in instances 2016-12-02 16:55:23 -08:00
Floris van Doorn
d12a2a264b fix(hott:group_theory): change group to has_mul 2016-12-02 16:55:23 -08:00
Floris van Doorn
d5a72f6327 feat(homotopy_group): use is_succ for homotopy groups 
Now you can use πg[n] as long as Lean can find an instance that n is a successor, you don't have to always write πg[k+1]
 2016-09-22 16:00:27 -04:00
Floris van Doorn
341a53b880 feat(pointed): make the naming in the pointed library more consistent. 
Also start on a naming conventions file
 2016-09-22 16:00:27 -04:00
Floris van Doorn
554abe88c2 feat(hott/algebra): define bundled additive groups as multiplicative groups 2016-09-19 22:13:42 -04:00
Floris van Doorn
c884e7bbb9 feat(hott/algebra): define additive structures to be multiplicative structures 2016-09-19 22:13:35 -04:00
Floris van Doorn
8d6010ccad feat(pointed): use pointed equivalences instead of equalities for some lemmas 2016-09-18 02:14:32 -04:00
Floris van Doorn
e2734080c6 fix(algebra): change the reducibility of some defintions 2016-09-18 02:14:32 -04:00
Floris van Doorn
11c08c51e6 fix(algebra/group_theory): split homomorphisms into additive and multiplicative homomorphisms 2016-09-18 02:14:31 -04:00
Floris van Doorn
c68e013fcb refactor(fin+nat): move is_succ to nat 2016-09-18 02:14:25 -04:00
Floris van Doorn
d70334d100 feat(hott/algebra/bundled): add a parameter to Group to specify whether it's an additive or multiplicative group 2016-09-18 02:13:30 -04:00
Floris van Doorn
467001c0a9 feat(hott): minor changes 2016-09-18 02:13:21 -04:00
Floris van Doorn
ddec6f77ee feat(category.pushout): finish second way of formulating universal property 2016-09-18 02:13:03 -04:00
Floris van Doorn
fd5adb831b feat(category.pushout): finish universal property of pushout 
In the previous commit there was still one step missing: that the natural isomorphisms are also unique.
 2016-09-17 17:05:46 -04:00
Floris van Doorn
fe1fbae540 feat(category.pushout): give the universal property of the pushout of categories 2016-09-17 17:05:46 -04:00
Jakob von Raumer
c81c86a9b8 chore(hott) remove duplicate lemma, make defs private, update book.md 2016-09-08 19:34:54 -07:00
Jakob von Raumer
e79063970d feat(hott) finish proof of lemma 9.9.4 2016-09-08 19:34:54 -07:00
Jakob von Raumer
5f06496f89 feat(hott) almost finish 9.9.4 proof 2016-09-08 19:34:54 -07:00
Jakob von Raumer
3e1ee4b714 feat(hott) add functor axioms for lemma 9.9.4 construction 2016-09-08 19:34:54 -07:00
Jakob von Raumer
d26d98531c feat(hott) add morphism part of construction for lemma 9.9.4 2016-09-08 19:34:54 -07:00
Jakob von Raumer
8718a649c4 feat(hott) add first bit of proof of 9.9.4: construction of some gadgets and prove that they are contractible 2016-09-08 19:34:54 -07:00
Jakob von Raumer
143bd765f3 chore(hott) fix markup syntax in book.md 2016-09-08 19:34:54 -07:00
Jakob von Raumer
3416430cfa chore(hott) update book.md 2016-09-08 19:34:54 -07:00
Jakob von Raumer
548671ce1b feat(hott) prove lemma 9.9.2: essentially surjective and full functors induce fully faithful functors in the functor category 2016-09-08 19:34:54 -07:00
Jakob von Raumer
0ff8a96be1 feat(hott) formalize book lemma 9.9.1: essentially surjective functors induce faithful functors in the functor category 2016-09-08 19:34:54 -07:00
Jakob von Raumer
3de39200a4 chore(hott) update book.md and constructions.md to include rezk completion 2016-09-08 19:34:54 -07:00
Jakob von Raumer
cc70845332 chore(hott) update book.md and constructions.md to include rezk completion 2016-07-09 10:32:50 -07:00
Jakob von Raumer
18a27cf963 chore(hott) merge namespaces in rezk completion 2016-07-09 10:31:42 -07:00
Jakob von Raumer
82a8d137da feat(hott) prove that rezk functor is a weak equivalence 2016-07-09 10:31:42 -07:00
Jakob von Raumer
57bf0a09dd feat(hott) add rezk completion as univalent category 2016-07-09 10:31:42 -07:00
Jakob von Raumer
86d9a1c84d feat(hott) add id_of_iso of rezk completion 2016-07-09 10:31:42 -07:00
Jakob von Raumer
6d6ab3f36b feat(hott) instantiate rezk completion as precategory 2016-07-09 10:31:42 -07:00
Jakob von Raumer
64e1e5404c feat(hott) add composition for rezk completion 2016-07-09 10:31:41 -07:00
Jakob von Raumer
5c4aac6c8a feat(hott) add idenity for rezk completion 2016-07-09 10:31:41 -07:00
Jakob von Raumer
8d4ad591c8 feat(hott) add missing pathover lemmas 2016-07-09 10:31:41 -07:00
Jakob von Raumer
a5fe82f177 feat(hott) add carrier and hom set of rezk completion 2016-07-09 10:31:41 -07:00
Floris van Doorn
2cc8914874 feat(homotopy): add results about infty-connectedness and loops of EM-spaces 2016-07-09 10:20:22 -07:00
Floris van Doorn
3213b1b3b0 feat(EM): Prove some corollaries of Whitehead's principle, and prove that K(G,1) is unique. 
Also reorder the arguments of is_equiv_compose
 2016-07-09 10:20:22 -07:00
Floris van Doorn
17ccc283a9 feat(hott): move basic theorems from colimit development to library. 
Most notable changes:
rename apo011 -> apd011 and apd011 -> apdt011
make an argument of pathover_of_eq explicit
 2016-07-09 10:20:22 -07:00
Floris van Doorn
ae1b2e854c feat(hott): various minor changes 2016-07-09 10:20:21 -07:00
Floris van Doorn
fcf06ae2f5 feat(vankampen): prove the van Kampen theorem with basepoints 2016-07-09 10:20:21 -07:00
Floris van Doorn
15cdd593c1 feat(init.{equiv|ua}): remove duplicated theorem 2016-07-09 10:20:21 -07:00
Floris van Doorn
41de1a8271 feat(hit): add construction of propositional truncation to the library 2016-07-09 10:20:21 -07:00
Floris van Doorn
735230ad07 feat(hott): small changes, simplify van Kampen 2016-07-09 10:20:21 -07:00
Floris van Doorn
e96e4a677d feat(homotopy): prove the naive Seifert-Van Kampen theorem 
Also define the pushout of categories and the pushout of groupoids
 2016-07-09 10:20:21 -07:00
Floris van Doorn
61848c4a2e feat(hott): define pushout of groupoids 2016-07-09 10:20:21 -07:00
Floris van Doorn
9f13527c25 chore(hott): update default files and some markdown files 2016-07-09 10:20:21 -07:00
Floris van Doorn
dd5dcb1dd1 feat(hott): prove something without using ua and update book.md 2016-07-09 10:20:21 -07:00
Floris van Doorn
66ec690061 feat(book): add new theorems to book.md 2016-05-06 14:27:27 -07:00
Floris van Doorn
52dd6cf90b feat(hott): Port files from other repositories to the HoTT library. 
This commit adds truncated 2-quotients, groupoid quotients, Eilenberg MacLane spaces, chain complexes, the long exact sequence of homotopy groups, the Freudenthal Suspension Theorem, Whitehead's principle, and the computation of homotopy groups of almost all spheres which are known in HoTT.
 2016-05-06 14:27:27 -07:00
Floris van Doorn
ab7adf3084 fix(pathover): remove unused argument of loop_pathover 2016-05-06 14:27:27 -07:00
Floris van Doorn
2afdaf6906 fix(groupoid): redefine groupoid given by a group 
The composition was in the reverse order
 2016-05-06 14:27:27 -07:00
Floris van Doorn
1135d80266 feat(hott): use group isomorphisms instead of equality between groups 2016-05-06 14:27:27 -07:00
Floris van Doorn
8db4676c46 feat(hott): various changes and additions in the HoTT library 
Add more theorems about mapping cylinders, fibers, truncated 2-quotient, truncated univalence, pre/postcomposition with an iso in a precategory.

renamings: equiv.refl -> equiv.rfl and equiv_eq <-> equiv_eq'
 2016-05-06 14:27:27 -07:00
Floris van Doorn
a6b5191be6 feat(pushout/susp): change definition of elim_type, so that flattening is easier to prove 2016-05-06 14:26:46 -07:00
Jakob von Raumer
651df51cb7 chore(hott) the coercion doesn't seem to be the problem 2016-04-11 09:45:59 -07:00
Jakob von Raumer
7a9e1c7f4f chore(hott) fix sum proof by adding manual coercions 2016-04-11 09:45:59 -07:00
Floris van Doorn
a6319118e3 feat(types.pointed): small additions 2016-04-11 09:45:59 -07:00
Floris van Doorn
f983724cf6 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
 2016-04-11 09:45:59 -07:00
Floris van Doorn
4895726c54 feat(connectedness): show that if f is n-connected, then trunc_functor k f is so, too 2016-04-11 09:45:59 -07:00
Floris van Doorn
54da5bcbda feat(hott): add some [constructor] attributes 2016-04-11 09:45:59 -07:00
Floris van Doorn
3887efa7c1 feat(hott): some renamings in init.path 2016-04-11 09:45:59 -07:00
Floris van Doorn
3240df6020 feat(book): add comments about chapter 10 2016-04-11 09:45:59 -07:00
Floris van Doorn
dc37ec954d refactor(hott): rename apdo to apd 2016-04-11 09:45:59 -07:00
Floris van Doorn
80a2e285cb feat(init/ua): add ua_symm and ua_trans 2016-04-11 09:45:59 -07:00
Floris van Doorn
05b59aecf8 refactor(hott): rename apd to apdt 2016-04-11 09:45:59 -07:00
Floris van Doorn
b1ed69f621 feat(hott): small changes, mostly in pointed2 2016-04-11 09:45:59 -07:00
Leonardo de Moura
226f8bafeb fix(library/tactic/rewrite_tactic): do not allow projections to be unfolded 
fixes #1032

This is just a workaround. A better fix has been implemented in the
lean3 branch.
 2016-03-28 13:02:57 -07:00
Ulrik Buchholtz
1c52062f1e chore(hott): standardize names of homotopy_of_inv_homotopy_post and friends 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
5257e282aa feat(hott/homotopy): additions to sphere and susp, improve quaternionc_hopf 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
7e8ba1440f feat(hott): update book.md and homotopy.md to reflect additions 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
f11169b8f2 feat(hott): the quaternionic hopf fibration 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
89296ec52a feat(hott): the complex hopf fibration S3 to S2 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
d53320cb0f feat(hott): the imaginaroid version of the cayley dickson construction 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
0b9084c7d2 feat(hott): hopf construction and delooping of K(G,1)s 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
bb64913e50 feat(hott): flattening lemma for susp 2016-03-23 09:22:55 -07:00
Ulrik Buchholtz
bd9e47c82c feat(hott): functoriality of pushout; connectedness in is_conn namespace 
other changes:
- move result about connectedness of susp to homotopy.susp
- improved definition of circle multiplication
- improved the interface to join
 2016-03-23 09:22:55 -07:00
Leonardo de Moura
5e14b4ebe8 fix(library,hott): avoid rewrite with patterns of the form (?M ...) 2016-03-09 15:39:17 -08:00
Floris van Doorn
003c11c917 feat(connectedness): is_conn_map -> is_conn_fun, and unbundle the P in elimination principles 2016-03-06 13:03:31 -05:00
Floris van Doorn
1e10810a1e feat(init/funext): add function extensionality as an axiom. 
This allows us to keep track of theorems which use function extensionality, but not full univalence
 2016-03-06 13:03:31 -05:00
Floris van Doorn
2d9c3985c9 feat(square): add variants of eq_pathover 2016-03-06 13:03:31 -05:00
Floris van Doorn
671ef077b9 feat(hott): additions, mostly to types.trunc 2016-03-06 13:03:31 -05:00
Floris van Doorn
5cacebcf86 feat(hott): replace assert by have and merge namespace equiv.ops into equiv 
The coercion A ≃ B -> (A -> B) is now in namespace equiv. The notation ⁻¹ for symmetry of equivalences is not supported anymore. Use ⁻¹ᵉ
 2016-03-03 10:13:21 -08:00
Floris van Doorn
058000f61d feat(homotopy/homotopy_group): add theorems in section 8.3 of the HoTT book 2016-03-03 10:13:21 -08:00
Floris van Doorn
1903601ba5 refactor(trunc): rename namespace is_trunc.trunc_index to trunc_index 2016-03-03 10:13:20 -08:00