Homotopy Type Theory
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Definition
As a twice-delooping of a pointed simply connected 2-groupoid
A pointed simply connected 2-groupoid consists of
- A type
- A basepoint
- A 1-connector
- A 2-truncator:
An abelian group or -module is the type of automorphisms of automorphisms in .
As a group
An abelian group or -module consists of
- A type ,
- A basepoint
- A binary operation
- A unary operation
- A contractible left unit identity
- A contractible right unit identity
- A contractible associative identity
- A contractible left inverse identity
- A contractible right inverse identity
- A contractible commutative identity
- A 0-truncator
As a module
An abelian group or -module is a set with a term and a binary function , and a left multiplicative -action , such that
We define the functions and to be
and is an abelian group and a -bimodule
Examples
- The
Every contractible magma with a function is an abelian group.
integers are an abelian group.
-
The integers are an abelian group.
See also
References
Revision on June 13, 2022 at 23:11:24 by
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