‣ 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 \(\beta\).
‣ IdentityTwoCell( alpha ) | ( attribute ) |
Returns: a \(2\)-cell
The argument is a morphism \(\alpha\). The output is its identity \(2\)-cell \(\mathrm{id}_{\alpha}: \alpha \rightarrow \alpha\).
‣ AddIdentityTwoCell( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation IdentityTwoCell. \(F: \alpha \mapsto \mathrm{id}_{\alpha}\).
‣ 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 \(d \ast c: (\gamma \circ \alpha) \rightarrow (\delta \circ \beta)\).
‣ AddHorizontalPreCompose( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation HorizontalPreCompose. \(F: (c,d) \mapsto d \ast c\).
‣ 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 \(d \ast c: (\gamma \circ \alpha) \rightarrow (\delta \circ \beta)\).
‣ AddHorizontalPostCompose( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation HorizontalPostCompose. \(F: (d,c) \mapsto d \ast c\).
‣ 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 \(d \circ c: \alpha \rightarrow \gamma\).
‣ AddVerticalPreCompose( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation VerticalPreCompose. \(F: (c,d) \mapsto d \circ c\).
‣ 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 \(d \circ c: \alpha \rightarrow \gamma\).
‣ AddVerticalPostCompose( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation VerticalPostCompose. \(F: (d,c) \mapsto d \circ c\).
‣ 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.
‣ AddIsWellDefinedForTwoCells( C, F ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operations adds the given function \(F\) to the category for the basic operation IsWellDefinedForTwoCells. \(F: c \mapsto \mathtt{IsWellDefinedForMorphisms}( c )\).
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