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[Merged by Bors] - feat(order/lattice): add complete_semilattice_Sup/Inf #6797
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semorrison
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Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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Looks reasonable to me bors d+ Probably worth merging master ifrst just in case this has gone stale, unless bors is idle anyway |
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This adds `complete_semilattice_Sup` and `complete_semilattice_Inf` above `complete_lattice`. This has not much effect, as in fact either implies `complete_lattice`. However it's useful at times to have these, when you can naturally define just one half of the structure at a time (e.g. the subobject lattice in a general category, where for `Sup` we need coproducts and images, while for the `Inf` we need wide pullbacks). There are many places in mathlib that currently use `complete_lattice_of_Inf`. It might be slightly nicer to instead construct a `complete_semilattice_Inf`, and then use the new `complete_lattice_of_complete_semilattice_Inf`, but I haven't done that here. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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This adds `complete_semilattice_Sup` and `complete_semilattice_Inf` above `complete_lattice`. This has not much effect, as in fact either implies `complete_lattice`. However it's useful at times to have these, when you can naturally define just one half of the structure at a time (e.g. the subobject lattice in a general category, where for `Sup` we need coproducts and images, while for the `Inf` we need wide pullbacks). There are many places in mathlib that currently use `complete_lattice_of_Inf`. It might be slightly nicer to instead construct a `complete_semilattice_Inf`, and then use the new `complete_lattice_of_complete_semilattice_Inf`, but I haven't done that here. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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This adds `complete_semilattice_Sup` and `complete_semilattice_Inf` above `complete_lattice`. This has not much effect, as in fact either implies `complete_lattice`. However it's useful at times to have these, when you can naturally define just one half of the structure at a time (e.g. the subobject lattice in a general category, where for `Sup` we need coproducts and images, while for the `Inf` we need wide pullbacks). There are many places in mathlib that currently use `complete_lattice_of_Inf`. It might be slightly nicer to instead construct a `complete_semilattice_Inf`, and then use the new `complete_lattice_of_complete_semilattice_Inf`, but I haven't done that here. Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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This adds
complete_semilattice_Supandcomplete_semilattice_Infabovecomplete_lattice.This has not much effect, as in fact either implies
complete_lattice. However it's useful at times to have these, when you can naturally define just one half of the structure at a time (e.g. the subobject lattice in a general category, where forSupwe need coproducts and images, while for theInfwe need wide pullbacks).There are many places in mathlib that currently use
complete_lattice_of_Inf. It might be slightly nicer to instead construct acomplete_semilattice_Inf, and then use the newcomplete_lattice_of_complete_semilattice_Inf, but I haven't done that here.