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

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

 * PM: category of sets, id=1895 -- WP: category of sets -- Status: A
 * — Blotwell 05:31, 3 September 2005 (UTC)


 * PM: functor, id=1093 -- WP: functor -- Status: A
 * — 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.)

 * 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

 * 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: source, id=8109new! -- WP guess: source -- 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

 * PM: precategory, id=8389new! -- WP guess: precategory -- Status:

18A15 Foundations, relations to logic and deductive systems

 * PM: well-pointed topos, id=8812new! -- WP guess: well-pointed topos -- Status:

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

 * PM: equalizer, id=6404 -- WP: equaliser -- Status: A
 * — Blotwell 05:31, 3 September 2005 (UTC)


 * PM: subobject, id=6399 -- WP: subobject -- Status: A
 * — 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.)

 * 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

 * 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.)

 * 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

 * PM: complete category, id=8373new! -- WP guess: complete category -- Status:

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

 * 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

 * PM: skeleton, id=9329new! -- WP guess: skeleton -- Status:

18B25 Topoi

 * 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

 * 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)

 * PM: preorder as a category, id=8971new! -- WP guess: preorder as a category -- Status:

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

 * 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:

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

 * PM: monad, id=2614 -- WP: monad (category theory) -- Status: A
 * — Blotwell 05:31, 3 September 2005 (UTC)


 * PM: comonad, id=8623new! -- WP guess: comonad -- Status:

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

 * PM: monoidal category, id=8681new! -- WP guess: monoidal category -- Status:

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

 * 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.)

 * PM: group object, id=5606 -- WP: group object -- Status: NM
 * — Blotwell 05:31, 3 September 2005 (UTC)

18E05 Preadditive, additive categories

 * 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

 * 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:

18E30 Derived categories, triangulated categories

 * PM: derived category, id=4016 -- WP: derived category -- Status: NM
 * — Blotwell 05:31, 3 September 2005 (UTC)

18E99 Miscellaneous

 * PM: enough injectives, id=4605 -- WP: injective object -- Status: NM
 * — Blotwell 05:31, 3 September 2005 (UTC)

18F20 Presheaves and sheaves

 * PM: presheaf, id=1105 -- WP: sheaf -- Status: A
 * — Blotwell 05:31, 3 September 2005 (UTC)


 * PM: ringed space, id=8426new! -- WP guess: ringed space -- Status:

18G10 Resolutions; derived functors

 * 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

 * 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)

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

 * 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

 * 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

 * 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

 * 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)