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batching together convention adaptations

Co-authored-by: Fredrik Bakke <[email protected]>
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djspacewhale and fredrik-bakke authored Feb 15, 2025
1 parent 97a5669 commit 8e37ed8
Showing 1 changed file with 26 additions and 16 deletions.
42 changes: 26 additions & 16 deletions src/quasigroups/loops.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -96,11 +96,16 @@ module _

is-prop-has-left-unit-Quasigroup : is-prop has-left-unit-Quasigroup
pr1 (is-prop-has-left-unit-Quasigroup e f) =
eq-type-subtype is-left-unit-Quasigroup-Prop
(left-units-agree-Quasigroup e f)
pr2 (is-prop-has-left-unit-Quasigroup e f) p =
is-set-has-uip (is-set-type-subtype is-left-unit-Quasigroup-Prop
(is-set-Quasigroup Q)) e f (pr1 (is-prop-has-left-unit-Quasigroup e f)) p
eq-type-subtype
( is-left-unit-Quasigroup-Prop)
( left-units-agree-Quasigroup e f)
pr2 (is-prop-has-left-unit-Quasigroup e f) =
is-set-has-uip
( is-set-type-subtype is-left-unit-Quasigroup-Prop
( is-set-Quasigroup Q))
( e)
( f)
( pr1 (is-prop-has-left-unit-Quasigroup e f))
```

### Right units in quasigroups
Expand Down Expand Up @@ -142,11 +147,16 @@ module _

is-prop-has-right-unit-Quasigroup : is-prop has-right-unit-Quasigroup
pr1 (is-prop-has-right-unit-Quasigroup e f) =
eq-type-subtype is-right-unit-Quasigroup-Prop
(right-units-agree-Quasigroup e f)
pr2 (is-prop-has-right-unit-Quasigroup e f) p =
is-set-has-uip (is-set-type-subtype is-right-unit-Quasigroup-Prop
(is-set-Quasigroup Q)) e f (pr1 (is-prop-has-right-unit-Quasigroup e f)) p
eq-type-subtype
( is-right-unit-Quasigroup-Prop)
( right-units-agree-Quasigroup e f)
pr2 (is-prop-has-right-unit-Quasigroup e f) =
is-set-has-uip
( is-set-type-subtype is-right-unit-Quasigroup-Prop
( is-set-Quasigroup Q))
( e)
( f)
( pr1 (is-prop-has-right-unit-Quasigroup e f))
```

### Units in quasigroups
Expand All @@ -158,25 +168,25 @@ type of units is equivalent to the type of pairs of left and right units.
```agda
has-unit-Quasigroup : UU l
has-unit-Quasigroup =
Σ (type-Quasigroup Q)
λ e is-left-unit-Quasigroup e × is-right-unit-Quasigroup e
Σ ( type-Quasigroup Q)
( λ e is-left-unit-Quasigroup e × is-right-unit-Quasigroup e)

unit-has-unit-Quasigroup : has-unit-Quasigroup type-Quasigroup Q
unit-has-unit-Quasigroup (e , _) = e

has-unit-has-left-unit-Quasigroup :
has-unit-Quasigroup has-left-unit-Quasigroup
has-unit-has-left-unit-Quasigroup (e , e-left-unit , _) = e , e-left-unit
has-unit-has-left-unit-Quasigroup (e , e-left-unit , _) = (e , e-left-unit)

has-unit-has-right-unit-Quasigroup :
has-unit-Quasigroup has-right-unit-Quasigroup
has-unit-has-right-unit-Quasigroup (e , _ , e-right-unit) = e , e-right-unit
has-unit-has-right-unit-Quasigroup (e , _ , e-right-unit) = (e , e-right-unit)

has-unit-has-left-and-right-units-Quasigroup :
has-unit-Quasigroup has-left-unit-Quasigroup × has-right-unit-Quasigroup
has-unit-has-left-and-right-units-Quasigroup e =
(has-unit-has-left-unit-Quasigroup e) ,
(has-unit-has-right-unit-Quasigroup e)
( has-unit-has-left-unit-Quasigroup e) ,
( has-unit-has-right-unit-Quasigroup e)

left-and-right-units-agree-Quasigroup :
(e : has-left-unit-Quasigroup) (f : has-right-unit-Quasigroup)
Expand Down

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