0 the quality of having parts that match each other, especially in a way that is attractive, or similarity of shape or contents:
1 the quality of having parts on either side or half that match each other, esp. in an attractive way, or are the same size or shape
The last three categorical axioms are concerned with symmetries.
In particular the auxiliary tiles needed in all such formats can be characterized as the bidimensional counterparts of symmetries, duplicators and dischargers.
Because an equivalence is reflexive, they include all original symmetries.
The following representation theorem states the correspondence between double symmetries and ordinary symmetries.
The helical symmetries of these filaments are the same irrespective of the original flagellin species.
The notion of symmetries plays a key role for the establishment of the result.
Here we study some of their basic properties, such as metric properties, symmetries, and spectral properties.
Nonlinearizable holomorphic dynamics having an uncountable number of symmetries.
