‣ 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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