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
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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
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
17ccc283a9
feat(hott): move basic theorems from colimit development to library.
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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
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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
8db4676c46
feat(hott): various changes and additions in the HoTT library
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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
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
cc8d9bc7ff
refactor(hott): replace 'assert'-expr with 'have'-expr
2016-02-29 12:11:17 -08:00
Leonardo de Moura
5a4dd3f237
feat(library/reducible): remove [quasireducible] annotation
2016-02-25 17:42:44 -08:00
Leonardo de Moura
510168a387
refactor(library,hott): remove unnecessary annotations
2016-02-25 12:26:20 -08:00
Floris van Doorn
43cf2ad23d
style(hott): replace all other occurrences of hprop/hset
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They are replaced by either Prop/Set or prop/set
2016-02-22 11:15:38 -08:00
Floris van Doorn
4e2cc66061
style(*): rename is_hprop/is_hset to is_prop/is_set
2016-02-22 11:15:38 -08:00
Floris van Doorn
9e492a8771
feat(category): more about adjoint functors
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This commit has multiple unfinished proofs (commented out)
2015-11-16 21:32:09 -08:00
Floris van Doorn
46dba4ee5e
refactor(category): move some files to subfolders, and create file with basic functors
2015-11-08 14:04:59 -08:00
Floris van Doorn
e14754a337
feat(category): start on proof of yoneda preserves limits and limit functor is left adjoint
2015-11-08 14:04:59 -08:00
Floris van Doorn
f2d07ca23c
feat(category): various small changes in category theory
2015-11-08 14:04:59 -08:00
Floris van Doorn
de1c47eda9
feat(categories): add exponential laws for categories
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also give nicer rules to construct equalities between (pre)categories
2015-11-08 14:04:59 -08:00
Floris van Doorn
0e7b7af1da
refactor(category): add new folder functor, split adjoint file into separate files
2015-11-08 14:04:59 -08:00
Floris van Doorn
18ec5f8b85
feat(categories): prove introduction rule for equivalences
2015-11-08 14:04:58 -08:00
Floris van Doorn
448178a045
feat(category.functor2): prove that the category of functors is complete and cocomplete if the codomain is
2015-11-08 14:04:58 -08:00
Floris van Doorn
3b7afad6ad
feat(category.hset): prove that the category of sets is cocomplete
2015-11-08 14:04:58 -08:00
Floris van Doorn
c7fd29f854
feat(category): start with the introduction rule for equivalences
2015-11-08 14:04:58 -08:00
Leonardo de Moura
d1e111fd6c
fix(hott,frontends/lean,library,library/tactic): make sure we can still compile the HoTT library
2015-11-08 14:04:55 -08:00
Floris van Doorn
115dedbd1c
fix(hott): notation spacing and markdown files
2015-10-02 16:26:10 -07:00
Floris van Doorn
2264759060
feat(category): define colimits as dual of limits
2015-09-28 09:09:22 -07:00
Floris van Doorn
df73931a6d
feat(category.opposite): prove that the opposite of a univalent category is univalent
2015-09-28 09:09:22 -07:00
Floris van Doorn
099bd95ebd
feat(category.limits): prove that being complete is a mere proposition for categories
2015-09-28 09:09:22 -07:00
Floris van Doorn
51edd0ad1d
feat(category.constructions.hset): prove that the category of sets is complete
2015-09-28 09:09:22 -07:00
