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fix up image idea
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fredrik-bakke committed Dec 10, 2023
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13 changes: 7 additions & 6 deletions src/foundation/universal-property-image.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -39,9 +39,10 @@ open import foundation-core.whiskering-homotopies

## Idea

The {{#concept "image" Disambiguation="maps of types" Agda=is-image}} of a map
`f : A X` is the least [subtype](foundation-core.subtypes.md) of `X`
containing all the values of `f`.
The
{{#concept "universal property of the image" Disambiguation="maps of types" Agda=is-image}}
of a map `f : A X` states that the [image](foundation.images.md) is the least
[subtype](foundation-core.subtypes.md) of `X` containing all the values of `f`.

## Definition

Expand Down Expand Up @@ -250,9 +251,9 @@ abstract
{ A = (fiber f x)}
( fiber-emb-Prop m x)
( λ t
( map-hom-slice f (map-emb m) h (pr1 t)) ,
( ( inv (triangle-hom-slice f (map-emb m) h (pr1 t))) ∙
( pr2 t)))
( map-hom-slice f (map-emb m) h (pr1 t)) ,
( ( inv (triangle-hom-slice f (map-emb m) h (pr1 t))) ∙
( pr2 t)))

map-is-image-im :
{l1 l2 l3 : Level} {X : UU l1} {A : UU l2} {B : UU l3} (f : A X)
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