Tetracategories are the algebraic definition of higher category for the most general (i.e. weak) 4-categories.
By the discussion at k-tuply monoidal (n,r)-category a tetracategory with a single object may be regarded as the delooping of a monoidal tricategory. This is discussed in (Hoffnung).
tetracategory
The structure of a tetracategories was given by Todd Trimble.
Todd Trimble Notes on Tetracategories
A polished writeup of the definition appears in section 3.2 of
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