Wikipedia

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

< Wikipedia:WikiProject Mathematics‎ | PlanetMath Exchange

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
Retrieved from "https://en.wikipedia.org/w/index.php?title=Wikipedia:WikiProject_Mathematics/PlanetMath_Exchange/18-XX_Category_theory;_homological_algebra&oldid=1136064985"