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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeJul 10th 2019
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   Author: Mike Shulman
   Format: MarkdownItexI'm not sure that the definition on this page is correct. Despite how wrong it seems to a category theorist, I think the adjective "complete" in "cpo" usually refers only to a *countable* sort of completeness. According to [wikipedia](https://en.wikipedia.org/wiki/Complete_partial_order), a "cpo" can mean at least three different things dependent on context, but "never" a partial order that's actually complete as a category (i.e. a [[complete lattice]]). <a href="https://ncatlab.org/nlab/revision/diff/cpo/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/cpo/3">v3</a>, <a href="https://ncatlab.org/nlab/show/cpo">current</a>

   I’m not sure that the definition on this page is correct. Despite how wrong it seems to a category theorist, I think the adjective “complete” in “cpo” usually refers only to a countable sort of completeness. According to wikipedia, a “cpo” can mean at least three different things dependent on context, but “never” a partial order that’s actually complete as a category (i.e. a complete lattice).

   diff, v3, current

2. • CommentRowNumber2.
   • CommentAuthorAli Caglayan
   • CommentTimeJul 11th 2019
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   Author: Ali Caglayan
   Format: MarkdownItexI've never heard of cpos, but only $\omega$-cpos which are used to model recursion in simply typed lambda calculus.

   I’ve never heard of cpos, but only $\omega$-cpos which are used to model recursion in simply typed lambda calculus.

3. • CommentRowNumber3.
   • CommentAuthorSam Staton
   • CommentTimeJul 11th 2019
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   Author: Sam Staton
   Format: MarkdownItexI think people use "cpo" to mean either "$\omega$-cpo" or "dcpo". I don't think I've ever seen it used to mean complete lattice. The weird thing is that "cpo" doesn't seem to appear in the given reference, the AHS book.

   I think people use “cpo” to mean either “$\omega$-cpo” or “dcpo”. I don’t think I’ve ever seen it used to mean complete lattice. The weird thing is that “cpo” doesn’t seem to appear in the given reference, the AHS book.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJul 11th 2019
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexChanged to say that cpos are either dcpos or $\omega$-cpos. <a href="https://ncatlab.org/nlab/revision/diff/cpo/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/cpo/4">v4</a>, <a href="https://ncatlab.org/nlab/show/cpo">current</a>

   Changed to say that cpos are either dcpos or $\omega$-cpos.

   diff, v4, current

5. • CommentRowNumber5.
   • CommentAuthormaxsnew
   • CommentTimeOct 28th 2022
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   Author: maxsnew
   Format: MarkdownItexI added a cross-reference to [[CPO]] and it looks like there are actually two pages that afaict should just be merged: [[cpo]] and [[dcpo]]. What's the process for that?

   I added a cross-reference to CPO and it looks like there are actually two pages that afaict should just be merged: cpo and dcpo. What’s the process for that?

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 28th 2022
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   Author: Urs
   Format: MarkdownItexPlease do merge if indicated. The method is pedestrian, but not too bad: First, of course, decide which of the two to keep, and merge relevant material from the other into it, including redirects etc. This entails that also the other entry must be renamed, so that its previous name can be used to redirect to the entry that is being kept. We usually rename either to "`PreviousName > History`" or to "`emptyXYZ`" (the next would be `empty170`) There is no way to really delete the now redundant entry (unless one calls hard delete of orphaned entries on the server): it's regarded as deleted for practical purposes as soon as it is "orphaned", meaning that no links point to it, which should indeed be the case after the merge.

   Please do merge if indicated. The method is pedestrian, but not too bad:

   First, of course, decide which of the two to keep, and merge relevant material from the other into it, including redirects etc.

   This entails that also the other entry must be renamed, so that its previous name can be used to redirect to the entry that is being kept. We usually rename either to “PreviousName > History” or to “emptyXYZ” (the next would be empty170)

   There is no way to really delete the now redundant entry (unless one calls hard delete of orphaned entries on the server): it’s regarded as deleted for practical purposes as soon as it is “orphaned”, meaning that no links point to it, which should indeed be the case after the merge.