Jump to content

Wikipedia:WikiProject Mathematics/PlanetMath Exchange/18-XX Category theory; homological algebra

From Wikipedia, the free encyclopedia

This page provides a list of all articles available at PlanetMath in the following topic:

18-XX Category theory; homological algebra.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Jtwdog 04:37, 28 October 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Just the "tensor product" example might be worth adding. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Can't find these at all on WP, suggest that they belong in the Abelian category article. — Blotwell 05:31, 3 September 2005 (UTC)[reply]

18-01 Instructional exposition (textbooks, tutorial papers, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A05 Definitions, generalizations

[edit]
Is this really notable? Google turns up only PlanetMath and some incomprehensible nonmathematical weirdness. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
This is already explained vaguely in partially ordered set but the section could be improved. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Should be an example in functor category, but it deserves its own redirect from arrow category too. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Just a one-line definition, it should be included in the functor article and endofunctor should redirect there. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A10 Graphs, diagram schemes, precategories

[edit]

18A15 Foundations, relations to logic and deductive systems

[edit]

18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A22 Special properties of functors (faithful, full, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A25 Functor categories, comma categories

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A35 Categories admitting limits (complete categories), functors preserving limits, completions

[edit]

18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18A99 Miscellaneous

[edit]

18Axx General theory of categories and functors

[edit]

18B25 Topoi

[edit]

18B30 Categories of topological spaces and continuous mappings

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18B35 Preorders, orders and lattices (viewed as categories)

[edit]

18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18Bxx Special categories

[edit]

18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18Cxx Categories and theories

[edit]

18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories

[edit]

18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)

[edit]

18D35 Structured objects in a category (group objects, etc.)

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18Dxx Categories with structure

[edit]

18E05 Preadditive, additive categories

[edit]

18E10 Exact categories, abelian categories

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Jtwdog 04:47, 28 October 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Jtwdog 04:47, 28 October 2005 (UTC)[reply]

18E25 Derived functors and satellites

[edit]

18E30 Derived categories, triangulated categories

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18E99 Miscellaneous

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18Exx Abelian categories

[edit]

18F10 Grothendieck topologies

[edit]

18F20 Presheaves and sheaves

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18F25 Algebraic $K$-theory and $L$-theory

[edit]

18F30 Grothendieck groups

[edit]

18Fxx Categories and geometry

[edit]

18G05 Projectives and injectives

[edit]

18G10 Resolutions; derived functors

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G15 Ext and Tor, generalizations, Künneth formula

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G20 Homological dimension

[edit]

18G30 Simplicial sets, simplicial objects (in a category)

[edit]
We already have nerve of an open covering—I'm sure this is related somehow. Anyway, merits a link from nerve (disambiguation). — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G35 Chain complexes

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Chain complex needs a whole section about chain maps consisting of the content from the above three articles. Redirects from chain map and chain homotopy would be good too. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G40 Spectral sequences, hypercohomology

[edit]
Also redirect from Leray spectral sequence. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G60 Other (co)homology theories

[edit]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]
Jtwdog 04:56, 28 October 2005 (UTC)[reply]
Jtwdog 04:56, 28 October 2005 (UTC)[reply]
It's a not-especially-short proof. — Blotwell 05:31, 3 September 2005 (UTC)[reply]
Blotwell 05:31, 3 September 2005 (UTC)[reply]

18G99 Miscellaneous

[edit]

18Gxx Homological algebra

[edit]