Preserving products #
Constructions to relate the notions of preserving products and reflecting products to concrete fans.
In particular, we show that piComparison G f
is an isomorphism iff G
preserves
the limit of f
.
The map of a fan is a limit iff the fan consisting of the mapped morphisms is a limit. This
essentially lets us commute Fan.mk
with Functor.mapCone
.
Instances For
The property of preserving products expressed in terms of fans.
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The property of reflecting products expressed in terms of fans.
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If G
preserves products and C
has them, then the fan constructed of the mapped projection of a
product is a limit.
Instances For
If pi_comparison G f
is an isomorphism, then G
preserves the limit of f
.
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If G
preserves limits, we have an isomorphism from the image of a product to the product of the
images.
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The map of a cofan is a colimit iff the cofan consisting of the mapped morphisms is a colimit.
This essentially lets us commute Cofan.mk
with Functor.mapCocone
.
Instances For
The property of preserving coproducts expressed in terms of cofans.
Instances For
The property of reflecting coproducts expressed in terms of cofans.
Instances For
If G
preserves coproducts and C
has them,
then the cofan constructed of the mapped inclusion of a coproduct is a colimit.
Instances For
If sigma_comparison G f
is an isomorphism, then G
preserves the colimit of f
.
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If G
preserves colimits,
we have an isomorphism from the image of a coproduct to the coproduct of the images.