diff --git a/src/foundation/universal-property-fiber-products.lagda.md b/src/foundation/universal-property-fiber-products.lagda.md index e6afc47890..50a5befa1e 100644 --- a/src/foundation/universal-property-fiber-products.lagda.md +++ b/src/foundation/universal-property-fiber-products.lagda.md @@ -28,9 +28,9 @@ open import foundation-core.universal-property-pullbacks ## Idea -The {{#concept "fiberwise product" Disambiguation="types"}} of two families `P` and `Q` over a type `X` is the -family of types `(P x) × (Q x)` over `X`. Similarly, the fiber product of two -maps `f : A → X` and `g : B → X` is the type +The {{#concept "fiberwise product" Disambiguation="types"}} of two families `P` +and `Q` over a type `X` is the family of types `(P x) × (Q x)` over `X`. +Similarly, the fiber product of two maps `f : A → X` and `g : B → X` is the type `Σ X (λ x → fiber f x × fiber g x)`, which fits in a [pullback](foundation-core.pullbacks.md) diagram on `f` and `g`. diff --git a/src/foundation/universal-property-image.lagda.md b/src/foundation/universal-property-image.lagda.md index a6c881fe0b..1599b9b791 100644 --- a/src/foundation/universal-property-image.lagda.md +++ b/src/foundation/universal-property-image.lagda.md @@ -39,8 +39,9 @@ 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 "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`. ## Definition diff --git a/src/foundation/universal-property-propositional-truncation.lagda.md b/src/foundation/universal-property-propositional-truncation.lagda.md index e506ee07d6..b92212ebbc 100644 --- a/src/foundation/universal-property-propositional-truncation.lagda.md +++ b/src/foundation/universal-property-propositional-truncation.lagda.md @@ -36,9 +36,11 @@ open import foundation-core.type-theoretic-principle-of-choice ## Idea A map `f : A → P` into a [proposition](foundation-core.propositions.md) `P` is -said to satisfy the {{#concept "universal property of the propositional truncation" Agda=universal-property-propositional-truncation}} of -`A`, or is said to be a {{#concept "propositional truncation" Agda=is-propositional-truncation}} of `A`, if any map -`g : A → Q` into a proposition `Q` extends uniquely along `f`. +said to satisfy the +{{#concept "universal property of the propositional truncation" Agda=universal-property-propositional-truncation}} +of `A`, or is said to be a +{{#concept "propositional truncation" Agda=is-propositional-truncation}} of `A`, +if any map `g : A → Q` into a proposition `Q` extends uniquely along `f`. ## Definition