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227 commits

Author SHA1 Message Date
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
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
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
a5fe82f177 feat(hott) add carrier and hom set of rezk completion 2016-07-09 10:31:41 -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
fcf06ae2f5 feat(vankampen): prove the van Kampen theorem with basepoints 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
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
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
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
dc37ec954d refactor(hott): rename apdo to apd 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
5e14b4ebe8 fix(library,hott): avoid rewrite with patterns of the form (?M ...) 2016-03-09 15:39:17 -08:00
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
e2b31a9b33 feat(hott): remove multiple_instances attribute 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
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
Jakob von Raumer
1104537d02 chore(hott) adjust to new naming for pointed types and truncated types 2016-03-01 13:52:53 -08:00
Jakob von Raumer
11458f64fe feat(hott/algebra) add order categories 2016-03-01 13:52:53 -08:00
Leonardo de Moura
faa0031d4e refactor(library,hott): remove 'by+' and 'begin+' 2016-02-29 13:15:48 -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
101cf1ec4c feat(frontends/lean): remove difference between 'have' and 'assert' 2016-02-29 11:28:20 -08:00
Leonardo de Moura
5a4dd3f237 feat(library/reducible): remove [quasireducible] annotation 2016-02-25 17:42:44 -08:00
Leonardo de Moura
d501295ec1 refactor(algebra/binary): remove unnecessary annotations 2016-02-25 15:11:52 -08:00
Leonardo de Moura
768ba1c363 refactor(library/hott): remove more unnecessary annotations 2016-02-25 14:30:00 -08:00
Leonardo de Moura
510168a387 refactor(library,hott): remove unnecessary annotations 2016-02-25 12:26:20 -08:00
Sebastian Ullrich
3de216d302 chore(*.md): fix/remove broken links 2016-02-23 10:11:24 -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
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