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7 Bialgebroids as algebroids with more structure
 7.1 Properties
 7.2 Attributes
 7.3 Constructors
 7.4 GAP categories

7 Bialgebroids as algebroids with more structure

7.1 Properties

7.1-1 IsCocommutative
‣ IsCocommutative( B )( property )

Returns: true or false

Check whether the bialgebroid B is cocommutative.

7.1-2 IsHopfAlgebroid
‣ IsHopfAlgebroid( B )( property )

Returns: true or false

Check whether the antipode of B is actually an antipode.

7.2 Attributes

7.2-1 Counit
‣ Counit( B )( attribute )

Returns: a CAP functor

The counit of the bialgebroid B.

7.2-2 Comultiplication
‣ Comultiplication( B )( attribute )

Returns: a CAP functor

The comultiplication of the bialgebroid B.

7.3 Constructors

7.3-1 AddBialgebroidStructure
‣ AddBialgebroidStructure( A, counit, comult )( operation )

Returns: a CAP category

Add to the algebroid A a counit and a comultiplication using the defining records counit and comult, respectively.

7.3-2 AddAntipode
‣ AddAntipode( B, S )( operation )

Returns: a CAP category

Add to the bialgebroid B an antipode S.

7.4 GAP categories

7.4-1 IsBialgebroid
‣ IsBialgebroid( arg )( filter )

Returns: true or false

The GAP category of bialgebroids.

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