‣ Source( c ) | ( attribute ) |
Returns: a morphism
The argument is a 2-cell c: \alpha \rightarrow \beta. The output is its source \alpha.
‣ Range( c ) | ( attribute ) |
Returns: a morphism
The argument is a 2-cell c: \alpha \rightarrow \beta. The output is its range \beta.
‣ Target( c ) | ( attribute ) |
Returns: a morphism
The argument is a 2-cell c: \alpha \rightarrow \beta. The output is its target \beta.
‣ Add( category, twocell ) | ( operation ) |
Adds twocell as a 2-cell to category.
‣ AddTwoCell( category, twocell ) | ( operation ) |
Adds twocell as a 2-cell to category. If twocell already lies in the filter IsCapCategoryTwoCell, the operation Add (4.2-1) can be used instead.
‣ CreateCapCategoryTwoCellWithAttributes( category, source, range[, attr1, val1, attr2, val2, ...] ) | ( function ) |
Returns: a twocell
Creates a 2-cell in category with the given attributes.
‣ IdentityTwoCell( alpha ) | ( attribute ) |
Returns: a 2-cell
The argument is a morphism \alpha. The output is its identity 2-cell \mathrm{id}_{\alpha}: \alpha \rightarrow \alpha.
‣ HorizontalPreCompose( c, d ) | ( operation ) |
Returns: a 2-cell
The arguments are two 2-cells c: \alpha \rightarrow \beta, d: \gamma \rightarrow \delta between morphisms \alpha, \beta: a \rightarrow b and \gamma, \delta: b \rightarrow c. The output is their horizontal composition d \ast c: (\gamma \circ \alpha) \rightarrow (\delta \circ \beta).
‣ HorizontalPostCompose( d, c ) | ( operation ) |
Returns: a 2-cell
The arguments are two 2-cells d: \gamma \rightarrow \delta, c: \alpha \rightarrow \beta between morphisms \alpha, \beta: a \rightarrow b and \gamma, \delta: b \rightarrow c. The output is their horizontal composition d \ast c: (\gamma \circ \alpha) \rightarrow (\delta \circ \beta).
‣ VerticalPreCompose( c, d ) | ( operation ) |
Returns: a 2-cell
The arguments are two 2-cells c: \alpha \rightarrow \beta, d: \beta \rightarrow \gamma between morphisms \alpha, \beta, \gamma: a \rightarrow b. The output is their vertical composition d \circ c: \alpha \rightarrow \gamma.
‣ VerticalPostCompose( d, c ) | ( operation ) |
Returns: a 2-cell
The arguments are two 2-cells d: \beta \rightarrow \gamma, c: \alpha \rightarrow \beta between morphisms \alpha, \beta, \gamma: a \rightarrow b. The output is their vertical composition d \circ c: \alpha \rightarrow \gamma.
‣ IsWellDefinedForTwoCells( c ) | ( operation ) |
Returns: a boolean
The argument is a 2-cell c. The output is true if c is well-defined, otherwise the output is false.
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