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Updated TOC in global README
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peterlefanulumsdaine committed May 24, 2022
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2 changes: 1 addition & 1 deletion Makefile
Original file line number Diff line number Diff line change
Expand Up @@ -18,13 +18,13 @@ PACKAGES += CwDM
PACKAGES += TypeCat_CompCat
PACKAGES += OtherDefs
PACKAGES += Categories
PACKAGES += Articles
PACKAGES += Instances
PACKAGES += Csystems
PACKAGES += Bsystems
PACKAGES += Cubical
PACKAGES += Initiality
PACKAGES += TypeConstructions
PACKAGES += Articles
############################################
# other user options; see also build/Makefile-configuration-template
BUILD_COQ ?= no
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66 changes: 35 additions & 31 deletions README.md
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Expand Up @@ -46,35 +46,39 @@ We give an overview of the packages and refer to each package's README for detai

NOTE: this table of contents is not automatically updated, and may often be out of sync with the development.

* *Articles/*
* currently only two .v files with little content concerning ALV
* *Auxiliary/*
* General background definitions and results that might be upstreamed into UniMath/UniMath
* *Categories/*
* Background constructions and results on categories; might be upstreamed to UniMath/CategoryTheory
* *ALV1/*
* Definition of CwF’s (a la Fiore) and Split Type-Categories
* Construction of an equivalence of types between families structures and split type structures
* Construction of an equivalence of categories between families structures and split type structures
* Definition of relative universe structures
* Construction of an equivalence between families structures and relative universe structures on Yoneda
* Construction of a function from families structures on a category to families structures on its Rezk completion
* *Displayed_Cats/*
* Library on displayed categories: a toolbox for constructing and working with categories of multi-component structures
* after the integration into UniMath of most of the material, only very little remains
* *ALV2/*
* Construction of equivalences of categories between families structures and split type structures, using
displayed categories
* *Instances/*
* for the time being, only the result that presheaves form a type category (providing an "instance" of the concept)
* *Bsystems/*
* the implementation of Vladimir Voevodsky's notion of B system
* *Csystems/*
- *Auxiliary/*
- General background definitions and results, that could be upstreamed into UniMath/UniMath
- *RelUniv/*
- Definition and basic development of *relative universe structures*
- *CompCats/*
- Basic development of *comprehension categories* (though UniMath itself contains the basic definition)
- *TypeCat/*
- Definition and basic development of *type-categories*, including splitness, the (2-)category of type-categories, and extra logical structure on them
- *CwF/*
- Definition and basic development of *categories with families*, using the Fiore–Aowdey approach with representable (more precisely, *represented*) maps
- An equivalence between families structures and relative universe structures on Yoneda
- Construction of a function from families structures on a category to families structures on its Rezk completion
- *CwF_TypeCat/*
- Comparisons between CwF’s and split type-categories; specifically:
- equivalence of types between families structures and split type structures, as presented in Ahrens–Lumsdaine–Voevodsky 2017
- equivalence of categories between families structures and split type structures
- *OtherDefs/*
- Various other categorical structures used in the study of type theory, not yet developed here enough to warrant separate packages
- *Categories/*
- Background constructions and results on categories; might be upstreamed to UniMath/CategoryTheory
- *Instances/*
- concrete examples of the categorical structures considered
- so far, only the result that presheaves form a type-category
- *Csystems/*
* the implementation of Vladimir Voevodsky's notion of C system
* *Initiality/*
* the interpretation from the syntax of a small type theory into suitably-structured CwA’s
* (incomplete) the syntactic CwA of the type theory, and its initiality
* *OtherDefs/*
* Various other categorical structures used in the study of type theory

*WARNING: many files in this subdirectory are in a very rough state; use at your own risk.*
- *Bsystems/*
* the implementation of Vladimir Voevodsky's notion of B system
- *Cubical/*
- To be documented
- *Initiality/*
- the interpretation from the syntax of a small type theory into suitably-structured CwA’s
- (incomplete) the syntactic CwA of the type theory, and its initiality
- *TypeConstructions/*
- To be documented
- *Articles/*
- files corresponding to articles whose content is formalised here, linking results named in the articles to their formalisation in this development

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