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Categorical Semantics WG
Coq for UF
Coq Working Group
Definitional Equality
Formalized Homotopy Theory
Higher Inductive Types
Homotopy Type System
HomotopyGroupsOfSpheres
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Informal Type Theory
Logical Frameworks
Math in HoTT
Meaning Explanations
Modal type theory
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Open Problems
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Math in HoTT
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Page for the working group on math in HoTT. Please add what you're working on, or ideas, or descriptions of the ideas below.
Done
See
Formalized Homotopy Theory
What people are working on
See
Formalized Homotopy Theory
Descent theorem and toposes: Egbert
Sets and truncation: Bas and Egbert
Thorsten and students are working on 1truncations and the connection to Hedberg's theorem
Univalent categories (doing category theory nicely in HoTT): Mike, Benedikt, and Chris
Higher groupoids and quotient types: Steve/Guillaume/Thorsten at least
Idea for things to work on
homology: see the answer to the following question
http://mathoverflow.net/questions/78450/homologytheoryconstructedinahomotopyinvariantway
)
stable homotopy theory
Postnikov towers
Covering spaces and actions of fundamental groups on covering spaces
simple results in cohesive HoTT
limit sketches
start going through Lurie's book and formalizing things
formalizing higher category theory
See also the page on
Open Problems
and
Formalized Homotopy Theory
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What people are working on
Thorsten and students are working on 1truncations and the connection to Hedberg's theorem
Idea for things to work on
See also the page on Open Problems and Formalized Homotopy Theory