Wikipedia:WikiProject Mathematics/PlanetMath Exchange/18-XX Category theory; homological algebra
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:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- 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.
- 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
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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]
- PM: category of sets, id=1895 -- WP: category of sets -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: Grothendieck spectral sequence, id=1095 -- WP: Grothendieck spectral sequence -- Status: C
- Jtwdog 04:37, 28 October 2005 (UTC)
- PM: monic, id=1896 -- WP: monomorphism -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: natural equivalence, id=1893 -- WP: natural equivalence -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: representable functor, id=1092 -- WP: representable functor -- Status: NM
- Just the "tensor product" example might be worth adding. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: supplemental axioms for an Abelian category, id=1094 -- WP: Abelian category -- Status: NM
- Can't find these at all on WP, suggest that they belong in the Abelian category article. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: diagonal functor, id=8818new! -- WP guess: diagonal functor -- Status:
- PM: equivalent definition of a representable functor, id=7788new! -- WP guess: equivalent definition of a representable functor -- Status:
- PM: identity functor, id=8817new! -- WP guess: identity functor -- Status:
- PM: monomorphisms of category of sets, id=8927new! -- WP guess: monomorphisms of category of sets -- Status:
18-01 Instructional exposition (textbooks, tutorial papers, etc.)[edit]
- PM: category theory, id=5622 -- WP: category theory -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: bibliography of category theory, id=8874new! -- WP guess: bibliography of category theory -- Status:
- PM: index of category theory, id=8873new! -- WP guess: index of category theory -- Status:
18A05 Definitions, generalizations[edit]
- PM: autofunctor, id=3560 -- WP: autofunctor -- Status: N
- Is this really notable? Google turns up only PlanetMath and some incomprehensible nonmathematical weirdness. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: automorphism, id=4529 -- WP: automorphism -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: category, id=965 -- WP: category (mathematics) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: category associated to a partial order, id=5618 -- WP: partially ordered set -- Status: NM
- This is already explained vaguely in partially ordered set but the section could be improved. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: category example (arrow category), id=2983 -- WP: functor category -- Status: NM
- Should be an example in functor category, but it deserves its own redirect from arrow category too. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: category isomorphism, id=5852 -- WP: isomorphism of categories -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: commutative diagram, id=3962 -- WP: commutative diagram -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: diagonal embedding, id=5817 -- WP: diagonal embedding -- Status: NC
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: dual category, id=2689 -- WP: dual category -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: duality principle, id=2688 -- WP: categorical duality -- Status: NC
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: endofunctor, id=2609 -- WP: functor -- Status: NM
- 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)
- PM: epi, id=6507 -- WP: epimorphism -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: examples of initial objects and terminal objects and zero objects, id=3132 -- WP: initial object -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: forgetful functor, id=2910 -- WP: forgetful functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: natural transformation, id=1570 -- WP: natural transformation -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: subcategory, id=5850 -- WP: subcategory -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: zero object, id=2864 -- WP: zero object -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: algebra formed from a category, id=8686new! -- WP guess: algebra formed from a category -- Status:
- PM: alternative definition of category, id=8845new! -- WP guess: alternative definition of category -- Status:
- PM: category of matrices, id=8712new! -- WP guess: category of matrices -- Status:
- PM: concrete category, id=8118new! -- WP guess: concrete category -- Status:
- PM: discrete category, id=8357new! -- WP guess: discrete category -- Status:
- PM: endomorphism, id=7462new! -- WP guess: endomorphism -- Status:
- PM: extremal monomorphism, id=8116new! -- WP guess: extremal monomorphism -- Status:
- PM: initial source, id=8110new! -- WP guess: initial source -- Status:
- PM: isomorphism-closed subcategory, id=8112new! -- WP guess: isomorphism-closed subcategory -- Status:
- PM: monoid as a category, id=8111new! -- WP guess: monoid as a category -- Status:
- PM: multifunctor, id=8819new! -- WP guess: multifunctor -- Status:
- PM: product of categories, id=8816new! -- WP guess: product of categories -- Status:
- PM: properties of monomorphisms and epimorphisms, id=8115new! -- WP guess: properties of monomorphisms and epimorphisms -- Status:
- PM: properties of regular and extremal monomorphisms, id=8117new! -- WP guess: properties of regular and extremal monomorphisms -- Status:
- PM: types of morphisms, id=8114new! -- WP guess: types of morphisms -- Status:
- PM: wellpowered category, id=8113new! -- WP guess: wellpowered category -- Status:
18A10 Graphs, diagram schemes, precategories[edit]
- PM: precategory, id=8389new! -- WP guess: precategory -- Status:
18A15 Foundations, relations to logic and deductive systems[edit]
- PM: well-pointed topos, id=8812new! -- WP guess: well-pointed topos -- Status:
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms[edit]
- — Blotwell 05:31, 3 September 2005 (UTC)
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: monomorphisms are pullback stable, id=7633new! -- WP guess: monomorphisms are pullback stable -- Status:
- PM: power object, id=7630new! -- WP guess: power object -- Status:
- PM: proof that an equalizer is a monomorphism, id=7627new! -- WP guess: proof that an equalizer is a monomorphism -- Status:
18A22 Special properties of functors (faithful, full, etc.)[edit]
- PM: exact functor, id=1362 -- WP: exact functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: faithful functor, id=5849 -- WP: faithful functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: full functor, id=5848 -- WP: full functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: essentially surjective, id=7104new! -- WP guess: essentially surjective -- Status:
18A25 Functor categories, comma categories[edit]
- PM: Yoneda embedding, id=1638 -- WP: Yoneda lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: comma category, id=8347new! -- WP guess: comma category -- Status:
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)[edit]
- PM: categorical direct product, id=2855 -- WP: product (category theory) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: categorical direct product is an inverse limit, id=5620 -- WP: product (category theory) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: categorical direct sum, id=2859 -- WP: coproduct -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: categorical pullback, id=5579 -- WP: categorical pullback -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: direct limit, id=5619 -- WP: limit (category theory) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: kernel is an inverse limit, id=5621 -- WP: kernel (category theory) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: attaching pullback squares, id=9461new! -- WP guess: attaching pullback squares -- Status:
- PM: direct limit of sets, id=9127new! -- WP guess: direct limit of sets -- Status:
- PM: limiting cone, id=8355new! -- WP guess: limiting cone -- Status:
18A35 Categories admitting limits (complete categories), functors preserving limits, completions[edit]
- PM: complete category, id=8373new! -- WP guess: complete category -- Status:
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)[edit]
- PM: adjoint functor, id=2691 -- WP: adjoint functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: equivalence of categories, id=4067 -- WP: equivalence of categories -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: reflective subcategory, id=9524new! -- WP guess: reflective subcategory -- Status:
- PM: unit of adjunction, id=9806new! -- WP guess: unit of adjunction -- Status:
- PM: universal mapping property, id=7566new! -- WP guess: universal mapping property -- Status:
18A99 Miscellaneous[edit]
18Axx General theory of categories and functors[edit]
18B25 Topoi[edit]
- PM: natural numbers object, id=8806new! -- WP guess: natural numbers object -- Status:
- PM: subobject classifier, id=8805new! -- WP guess: subobject classifier -- Status:
18B30 Categories of topological spaces and continuous mappings[edit]
- PM: category of pointed topological spaces, id=5315 -- WP: pointed space -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
18B35 Preorders, orders and lattices (viewed as categories)[edit]
- PM: preorder as a category, id=8971new! -- WP guess: preorder as a category -- Status:
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)[edit]
- PM: groupoid (category theoretic), id=3575 -- WP: groupoid -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: topological groupoid, id=6149 -- WP: topological groupoid -- Status: NC
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: category of paths on a graph, id=8992new! -- WP guess: category of paths on a graph -- Status:
18Bxx Special categories[edit]
18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples[edit]
- PM: monad, id=2614 -- WP: monad (category theory) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
18Cxx Categories and theories[edit]
18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories[edit]
- PM: monoidal category, id=8681new! -- WP guess: monoidal category -- Status:
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)[edit]
- PM: Cartesian closed category, id=8802new! -- WP guess: Cartesian closed category -- Status:
- PM: exponential object, id=8801new! -- WP guess: exponential object -- Status:
18D35 Structured objects in a category (group objects, etc.)[edit]
- PM: group object, id=5606 -- WP: group object -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
18Dxx Categories with structure[edit]
18E05 Preadditive, additive categories[edit]
- PM: additive category, id=7922new! -- WP guess: additive category -- Status:
- PM: preadditive category, id=7913new! -- WP guess: preadditive category -- Status:
18E10 Exact categories, abelian categories[edit]
- PM: abelian category, id=2865 -- WP: abelian category -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: enough projectives, id=6506 -- WP: enough projectives -- Status: C
- Jtwdog 04:47, 28 October 2005 (UTC)
- PM: exact sequence, id=2872 -- WP : exact sequence -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: projective object, id=6437 -- WP: projective object -- Status: C
- Jtwdog 04:47, 28 October 2005 (UTC)
- PM: examples of abelian categories, id=8931new! -- WP guess: examples of abelian categories -- Status:
- PM: proof that abelian groups form an abelian category, id=8932new! -- WP guess: proof that abelian groups form an abelian category -- Status:
18E25 Derived functors and satellites[edit]
18E30 Derived categories, triangulated categories[edit]
- PM: derived category, id=4016 -- WP: derived category -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
18E99 Miscellaneous[edit]
- PM: enough injectives, id=4605 -- WP: injective object -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
18Exx Abelian categories[edit]
18F10 Grothendieck topologies[edit]
18F20 Presheaves and sheaves[edit]
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: ringed space, id=8426new! -- WP guess: ringed space -- Status:
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]
- PM: derived functor, id=4017 -- WP: derived functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: delta functor, id=7317new! -- WP guess: delta functor -- Status:
- PM: horseshoe lemma, id=7799new! -- WP guess: horseshoe lemma -- Status:
18G15 Ext and Tor, generalizations, Künneth formula[edit]
- PM: Ext, id=4588 -- WP: Ext functor -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: Tor, id=6090 -- WP: Tor functor -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
18G20 Homological dimension[edit]
18G30 Simplicial sets, simplicial objects (in a category)[edit]
- PM: nerve, id=3453 -- WP: nerve of a category -- Status: NC
- 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)
- PM: simplicial category, id=3367 -- WP: simplicial category -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: simplicial object, id=3368 -- WP: simplicial object -- Status: NC
- — Blotwell 05:31, 3 September 2005 (UTC)
18G35 Chain complexes[edit]
- PM: 5-lemma, id=4598 -- WP: Five lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: 9-lemma, id=4597 -- WP: Nine lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: chain homotopy, id=1572 -- WP: chain complex -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: chain homotopy equivalence, id=6525 -- WP: chain complex -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: chain map, id=1571 -- WP: chain complex -- Status: NM
- 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)
- PM: homology (chain complex), id=3721 -- WP: homology (mathematics) -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: proof of 5-lemma, id=6568 -- WP: Five lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: snake lemma, id=3745 -- WP: snake lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: proof of snake lemma, id=5578 -- WP: snake lemma -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: proof of 9-lemma, id=8930new! -- WP guess: proof of 9-lemma -- Status:
18G40 Spectral sequences, hypercohomology[edit]
- PM: Leray spectral sequence, id=1099 -- WP: Leray-Serre spectral sequence -- Status: NC
- Also redirect from Leray spectral sequence. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: spectral sequence, id=4637 -- WP: spectral sequence -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
18G60 Other (co)homology theories[edit]
- PM: acyclic sheaf, id=6332 -- WP: acyclic -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: Cech cohomology group, id=6346 -- WP: Čech cohomology -- Status: A
- — Blotwell 05:31, 3 September 2005 (UTC)
- PM: De Rham-Weil theorem, id=6333 -- WP: De Rham-Weil theorem -- Status: C
- Jtwdog 04:56, 28 October 2005 (UTC)
- PM: Leray's theorem, id=6328 -- WP: Leray's theorem -- Status: C
- Jtwdog 04:56, 28 October 2005 (UTC)
- PM: proof of Leray's Theorem (via spectral sequences), id=6329 -- WP: Leray's theorem -- Status: N
- It's a not-especially-short proof. — Blotwell 05:31, 3 September 2005 (UTC)
- PM: Resolution of a Sheaf, id=6334 -- WP: Injective resolution -- Status: NM
- — Blotwell 05:31, 3 September 2005 (UTC)