Homotopy Type Theory
commutative A3-space > history (Rev #6, changes)
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Idea
The commutative version of the A3-space up to homotopy, without any higher commutative coherences.
Definition
A commutative -space or commutative -algebra in homotopy types or commutative H-monoid consists of
- A type ,
- A basepoint
- A binary operation
- A left unitor
- A right unitor
- An asssociator
- A commutator
Homomorphisms of commutative -spaces
A homomorphism of commutative -spaces between two commutative -spaces and is consists a of function such that
The basepoint is preservedA function such that
- The basepoint is preserved
- The binary operation is preserved
The binary operation is preservedA function
such that the left unitor is preserved:
such that the right unitor is preserved:
such that the associator is preserved:
such that the commutator is preserved:
Tensor product of commutative -spaces
(…)
Tensor product of commutative -spaces
(…)
Examples
-
The integers are a commutative -space.
-
A commutative monoid is a 0-truncated commutative -space.
-
A H-rig? is a -algebra in commutative -spaces.
See also
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