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

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

18-XX Category theory; homological algebra.

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

— 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.)

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

18A05 Definitions, generalizations

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

18A10 Graphs, diagram schemes, precategories

18A15 Foundations, relations to logic and deductive systems

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

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

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

— 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

— 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.)

— 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

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

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

18A99 Miscellaneous

18Axx General theory of categories and functors

18B25 Topoi

18B30 Categories of topological spaces and continuous mappings

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

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

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

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

18Bxx Special categories

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

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

18Cxx Categories and theories

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

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

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

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

18Dxx Categories with structure

18E05 Preadditive, additive categories

18E10 Exact categories, abelian categories

— 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

18E30 Derived categories, triangulated categories

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

18E99 Miscellaneous

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

18Exx Abelian categories

18F10 Grothendieck topologies

18F20 Presheaves and sheaves

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

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

18F30 Grothendieck groups

18Fxx Categories and geometry

18G05 Projectives and injectives

18G10 Resolutions; derived functors

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

18G15 Ext and Tor, generalizations, Künneth formula

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

18G20 Homological dimension

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

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

— 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

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

— 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

18Gxx Homological algebra

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