ogposets.OgMapPair

class rewalt.ogposets.OgMapPair(fst, snd)

Bases: tuple

Class for pairs of maps of oriented graded posets.

This is used as the argument and/or return type of pushouts and coequalisers, which play a prominent role in the theory.

Parameters

fst (OgMap) – The first map in the pair.
snd (OgMap) – The second map in the pair.

Methods

`coequaliser`(**params)	Returns the coequaliser of a parallel pair of total maps, if it exists.
`pushout`(**params)	Returns the pushout of a span of total maps, if it exists.
`then`(other, *others)	Returns the composite with other maps or pairs of maps of oriented graded posets, when defined.

Attributes

`fst`	Returns the first map in the pair.
`iscospan`	Returns whether the pair is a cospan (has a common target).
`isinjective`	Returns whether both maps are injective.
`isparallel`	Returns whether the pair is parallel (both a span and a cospan).
`isspan`	Returns whether the pair is a span (has a common source).
`issurjective`	Returns whether both maps are surjective.
`istotal`	Returns whether both maps are total.
`snd`	Returns the second map in the pair.
`source`	Returns the pair of sources of the pair of maps, or, if a span, their common source.
`target`	Returns the pair of targets of the pair of maps, or, if a cospan, their common target.

property fst

Returns the first map in the pair.

Returns: fst – The first map in the pair.
Return type: OgMap

property snd

Returns the second map in the pair.

Returns: snd – The second map in the pair.
Return type: OgMap

property source

Returns the pair of sources of the pair of maps, or, if a span, their common source.

Returns: source – The source or sources of the pair.
Return type: OgMap | tuple[OgMap]

property target

Returns the pair of targets of the pair of maps, or, if a cospan, their common target.

Returns: target – The target or targets of the pair.
Return type: OgMap | tuple[OgMap]

property isspan

Returns whether the pair is a span (has a common source).

Returns: isspan – True if and only if the pair is a span.
Return type: bool

property iscospan

Returns whether the pair is a cospan (has a common target).

Returns: iscospan – True if and only if the pair is a cospan.
Return type: bool

property isparallel

Returns whether the pair is parallel (both a span and a cospan).

Returns: isparallel – True if and only if the pair is parallel.
Return type: bool

property istotal

Returns whether both maps are total.

Returns: istotal – True if and only if both maps are total.
Return type: bool

property isinjective

Returns whether both maps are injective.

Returns: isinjective – True if and only if both maps are injective.
Return type: bool

property issurjective

Returns whether both maps are surjective.

Returns: issurjective – True if and only if both maps are surjective.
Return type: bool

then(other, *others)

Returns the composite with other maps or pairs of maps of oriented graded posets, when defined.

If given two pairs, it composes the first map with the first map, and the second map with the second map. If given a pair and a map, it composes both maps in the pair with the map.

Parameters

other (OgMap | OgMapPair) – The first map or pair of maps to follow.
others (OgMap | OgMapPair, optional) – Any number of other maps or pair of maps to follow.

Returns

composite – The composite with all the other arguments.

Return type

OgMapPair

coequaliser(**params)

Returns the coequaliser of a parallel pair of total maps, if it exists.

Keyword Arguments: wfcheck (bool) – Check whether the coequaliser is well-defined.
Returns: coequaliser – The coequaliser of the pair of maps.
Return type: OgMap
Raises: ValueError – If the pair is not total and parallel.

pushout(**params)

Returns the pushout of a span of total maps, if it exists.

Pushouts do not always exist in the category of oriented graded posets and maps; however, pushouts of injective (total) maps do always exist.

Keyword Arguments: wfcheck (bool) – Check whether the pushout is well-defined.
Returns: pushout – The pushout cospan of the pair of maps.
Return type: OgMapPair
Raises: ValueError – If the pair is not total and a span.