The category of finite partial orders #
This defines FinPartOrd
, the category of finite partial orders.
Note: FinPartOrd
is not a subcategory of BddOrd
because finite orders are not necessarily
bounded.
TODO #
FinPartOrd
is equivalent to a small category.
Equations
- FinPartOrd.instCoeSortType = { coe := fun (X : FinPartOrd) => ↑X.toPartOrd }
@[simp]
Equations
- FinPartOrd.instInhabited = { default := FinPartOrd.of PUnit.{?u.3 + 1} }
Equations
- One or more equations did not get rendered due to their size.
Constructs an isomorphism of finite partial orders from an order isomorphism between them.
Equations
- FinPartOrd.Iso.mk e = { hom := ↑e, inv := ↑e.symm, hom_inv_id := ⋯, inv_hom_id := ⋯ }
Instances For
@[simp]
@[simp]
OrderDual
as a functor.
Equations
- One or more equations did not get rendered due to their size.
Instances For
@[simp]
The equivalence between FinPartOrd
and itself induced by OrderDual
both ways.
Equations
- One or more equations did not get rendered due to their size.