Thin categories, prosets as categories, and poset/toset/lattice

[zwang123]

This contains changes in #4242.
Probably will wait until the previous PR is merged so that I can fix some merge conflicts
Now it is the time.

Added

• toslat: A toset is a lattice
• endmndlem
• thinccic: In a thin category, two objects are isomorphic iff there are morphisms between them in both directions.
• postc: The converted category is a poset iff no distinct objects are isomorphic.
• oppcthin: The opposite of a thin category is thin.
• subthinc: A subcategory of a thin category is thin.
• functhinc, fullthinc, thincfth: (full) functors to thin categories; faithful functors from thin categories
• inpw: Two ways of expressing a collection of subsets
• posjidm, posmidm: Poset join/meet is idempotent.
• ipolub/ipoglb: LUB/GLB of inclusion poset.
• mreclat, mrelatlubALT, and mrelatglbALT: The inclusion poset for a Moore system is a complete lattice
• topclat, topdlat, and related
• And lots of other theorems supporting the above

Fixed

• Description for setc2ohom, latjidm, and latmidm; and others.
• Rename monepilem to mpbiran3d and added mpbiran4d.

Changed

• Moved to main
  • biadanid
  • tospos
  • tleile
  • tltnle

[benjub]

Suggested change

	$( In a Toset, less-than is equivalent to not inverse "less than or equal
	to" see ~ pltnle . (Contributed by Thierry Arnoux, 11-Feb-2018.) $)
	$( In a Toset, "less than" is equivalent to the negation of the converse of
	"less than or equal to", see ~ pltnle . (Contributed by Thierry Arnoux,
	11-Feb-2018.) $)

[zwang123]

5e42b6e

[zwang123]

Out of town now so could not edit before I come back…

[benjub]

Let's try and merge it soon. Do not add new theorems or ideas, and only fix open conversations and address existing remarks.

[zwang123]

Let's try and merge it soon. Do not add new theorems or ideas, and only fix open conversations and address existing remarks.

Won’t be back until 2 weeks later as mentioned in #4248 (comment)
Looks like those open conversations are easy fixes but it’s hard to do it on my end…

[benjub]

Let's try and merge it soon. Do not add new theorems or ideas, and only fix open conversations and address existing remarks.

Won’t be back until 2 weeks later as mentioned in #4248 (comment) Looks like those open conversations are easy fixes but it’s hard to do it on my end…

No worries. Since it's mostly in your mathbox, merge conflicts will be easily resolved. What I meant is that potential new developments should go in a separate PR (also for ease of review), and that new commits in this PR should be only to address existing comments.