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88 commits

Author SHA1 Message Date
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
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
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
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
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
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
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
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
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
dc37ec954d refactor(hott): rename apdo to apd 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
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
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
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
Floris van Doorn
af4ba3d2fb feat(hott): prove that the (n+1)-sphere is n-connected 2016-03-03 10:13:20 -08:00
Floris van Doorn
e515875464 feat(hott): various additions 2016-03-03 10:13:20 -08:00
Floris van Doorn
c6e628da12 feat(hott): more computation rules for trunc_index and use nats for Lemma 8.6.2 2016-03-03 10:13:20 -08:00
Floris van Doorn
e5d5ef9d55 feat(hott/library): various changes and additions. 
Most notably:
Give le.refl the attribute [refl]. This simplifies tactic proofs in various places.
Redefine the order of trunc_index, and instantiate it as weak order.
Add more about pointed equivalences.
 2016-03-03 10:13:20 -08:00
Floris van Doorn
4238fdd3d8 fix(hott): add missing links to markdown files 2016-03-03 10:13:20 -08:00
Leonardo de Moura
cc8d9bc7ff refactor(hott): replace 'assert'-expr with 'have'-expr 2016-02-29 12:11:17 -08:00
Leonardo de Moura
510168a387 refactor(library,hott): remove unnecessary annotations 2016-02-25 12:26:20 -08:00
Leonardo de Moura
146edde5b3 feat(library/class): mark instances as quasireducible by default 
quasireducible are also known as lazyreducible.

There is a lot of work to be done.
We still need to revise blast, and add a normalizer for type class
instances. This commit worksaround that by eagerly unfolding
quasireducible.
 2016-02-25 12:11:29 -08:00
Floris van Doorn
facd94a1b4 feat(hott): various changes 
more about pointed truncated types, including pointed sets.
also increase the priority of some basic instances that nat/num/pos_num/trunc_index have 0, 1 and + (in both libraries)
also move the notation + for sum into the namespace sum, to (sometimes) avoid overloading with add
 2016-02-22 11:15:38 -08:00
Floris van Doorn
087c44d614 style(hott): rename instances of pType using pfoo instead of Foo 
For example, the pointed suspension operation was called Susp before this commit, but now is called psusp
 2016-02-22 11:15:38 -08:00
Floris van Doorn
c64e5a114c feat(circle): add missing facts that the circle is 1-truncated and 0-connected 2016-02-22 11:15:38 -08:00
Floris van Doorn
bac6d99cc7 style(hott): rename Pointed to pType 
also rename sigma_equiv_sigma_id to sigma_equiv_sigma_right and similarly for pi
 2016-02-22 11:15:38 -08:00