Homotopy Type Theory characteristic > history (Rev #1)

Definition

Let AA be a \mathbb{Z}-algebra. Let us define the type

Σ n:n1=0\Sigma \coloneqq \sum_{n:\mathbb{N}} n \cdot 1 = 0

where \cdot is the left multiplicative \mathbb{Z}-action of AA. The characteristic of AA is defined as

char(A) n:Σnchar(A) \coloneqq \bigwedge_{n:\Sigma} n

where \bigwedge is the dependent/indexed greatest common divisor function in \mathbb{N}.

See also

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