Talk:Specialization preorder

On 26 September 2025, it was proposed that this article be moved from Specialization (pre)order to Specialization preorder. The result of the discussion was moved.

Specialization

Should x ≤ y be read "x is a specialization of y" or "y is a specialization of x"?

Hartshorne says the former Algebraic geometry (Ex 3.17 p.93). However the motivational paragraph seems to claim the latter. Actually, the paragraph appears to be self-contradictory. If first claims that y is more specific, but then uses an analogy with genus and species and generic points which indicates that x is more specific. Can anyone sort this out? -- Fropuff (talk) 05:25, 10 December 2007 (UTC)[reply]

"we say that x is a specialization of y and that y is a generization of x" Is the latter word correct, or should it be "generalization"? Also, are these preorders the 0-dimensional case of weak n-categories where the cells are points, paths, homotopies and so on? (Perhaps I am completely off-base here.) If so, a note near the end would be useful. 2001:984:9396:1:6C97:7703:246A:3C4A (talk) 22:32, 21 December 2016 (UTC)[reply]

Overemphasis on the direction of the preorder

It seems that some authors write $x\leq y$ to mean "x is a specialisation of y" while others use it to mean "y is a specialisation of x". Fine.

The current version of the "Definition and Motivation" section seems to put a huge emphasis on this trivial point. This makes it impossible to follow, because it's constantly weighing up the pros and cons of one convention versus the other, while at the same time trying to explain what they both mean. If someone's in the mood for editing, it would be a great help just to pick one and include a brief note somewhere - just once, preferably at the end - that some authors use the other convention.

Nathaniel Virgo (talk) 20:23, 18 March 2020 (UTC)[reply]

Requested move 26 September 2025

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: moved. (closed by non-admin page mover) JuniperChill (talk) 09:24, 3 October 2025 (UTC)[reply]

Specialization (pre)order → Specialization preorder – Parentheses around the prefix "pre" are unnecessary, because the specialization preorder is still a preorder even if it happens to be an order (in the case of T0 spaces). GTrang (talk) 00:29, 26 September 2025 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.