User:Siddharthist

These are pages and sections I've written at least half of.

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• Category theory:
• Free category
• List object
• Template:Category theory
• Computer science:
• :Category:Streaming algorithms
• Misra-Gries summary
• Polynomial functor (type theory)
• E-graph
• Hyperproperty
• Soufflé (programming language)
• Path explosion
• Polyvariance
• Disjunctive Datalog
• LogicBlox
• Worst-case optimal join algorithm
• Syntax and semantics of logic programming
• Comparison of data structures
• Cooperating Validity Checker
• Constrained Horn clauses
• Topology:
• Configuration space (mathematics)
• Cubical complex
• Representation theory:
• Category of representations
• Frobenius–Schur indicator
• Frobenius reciprocity
• Tensor product of representations

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• Mathematics:
• Function space#In linear algebra
• Maschke's theorem#Formulations
• Monad (category theory)#Monads used in functional programming
• Computer science:
• Inductive type#W- and M-types
• Maximum satisfiability problem#Weighted MAX-SAT
• Smallest-circle problem#Welzl's algorithm
• Shortest common supersequence problem#Shortest common superstring
• Negligible function#Closure properties
• Chosen-plaintext attack#One-time pads
• Datalog#Syntax
• Datalog#Semantics
• Datalog#Evaluation
• Pointer analysis#Flow-insensitive approaches
• Abstract interpretation#Machine word abstract domains
• Fuzzing#List of popular fuzzers
• Program synthesis#Syntax-guided synthesis
• Coq (software)#Tactic language
• Formal methods#Solvers and competitions
• Satisfiability modulo theories#Relationship to automated theorem proving
• Satisfiability modulo theories#Decidable theories
• Proof assistant#Notable formalized proofs
• Philosophy:
• The Foundations of Arithmetic#Mill
• Temporal logic#Prior's tense logic (TL)

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• Template:Category theory
• Template:Program analysis

• Draft:Fundamental groupoid
• Draft:Universe (type theory)

The following are some edits I'd like to make but haven't yet.

These should take ten minutes or less.

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• Improve hash consing
• Add more properties to Opposite category
• Replace diagrams on initial topology and final topology with SVGs
• Add a citation to Awodey for the diagonal functor
• Add weak higher groupoid associator to the examples on Coherence condition
• Add examples of generated groups to Generating set of a group and Finitely generated group
• Maybe note that all examples in "Finitely generated" are examples of "Generating set" and all examples of presentations on Presentation of a group are also examples of generating sets?
• Add Lambek's Lemma to Initial algebra

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These should take a half hour or less.

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• Create Property-based testing (see Software testing#Property testing)
• Create page on Hypothesis Python library
• Clean up https://en.wikipedia.org/wiki/Symbolic_execution#Tools
• Add examples to Initial algebra and Final coalgebra
• Add the weighted approximation to Set cover problem
• Add the example of vertex cover to Linear programming relaxation
• Expand Real representation with Liebeck
• Add the application to mere propositions to subterminal object, add properties from nLab ({{nlab|id=subterminal+object|title=subterminal object}}), add Johnstone's topos theory as a reference.
• More fully split top type from singly rooted hierarchy. The former should contain information on type theoretical subtyping, whereas the latter should contain information on inheritance. They should both have paragraphs in their introductions distinguishing between the two.
• Semi-streaming algorithms
• Improve Calculus of constructions with descriptions of CIC, C(co)IC, [https://lirias.kuleuven.be/bitstream/123456789/513812/3/PCuIC.pdf pCuIC], etc.
• Add Misra-Gries to Element distinctness problem
• Improve Complex conjugate representation. Is it related to the dual representation?
• Add a "History" section to Betti number, based on Emmy Noether
• Add a "Formal definition" section to Free abelian group
• Create Draft:Path space, based on Glossary of algebraic topology#path space, https://ncatlab.org/nlab/show/path+space, and Homotopy type theory
• Add citations to Section (category theory)
• Read Lee's definition of Reduced homology and possibly add it as a reference on that page
• Verify the ring axioms in the definition of Group ring
• Expand coinduction (reference: Coqart)
• (After the new year 2018): Merge Category algebra into higher-dimensional algebra, or delete it.

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There are many pages on category theory that are extremely short, but I am not very familiar with the concepts.

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• Anafunctor
• Category of categories
• 2-functor
• Tensor-hom adjunction
• Natural number object
• Improve the end of Direct sum
• Investigate the relationship between Congruence (abstract algebra) and equalizers.
• Justify Top as a Distributive category
• Add properties to Distributive category
• Add a section on the free groupoid to the Free category page. References on nLab.{{Cite web|url=https://ncatlab.org/nlab/show/free+groupoid|title=free groupoid in nLab|website=ncatlab.org|access-date=2017-09-13}}
• Add the fundamental groupoid of a path-connected space as an example of a Connected category
• Simpler examples of Isomorphism of categories
• Add section "In homotopy type theory" to Category (mathematics), discussing the difference between "precategories" and univalent categories.
• Rewrite the definition of a Group object to be less steeped in category theoretical vocabulary and conventions
• Improve Church–Rosser theorem

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• Create a section on Pointer analysis with CFL reachability: https://ieeexplore.ieee.org/abstract/document/6957254
• Create SV-COMP
• Create a section about decidability on Separation logic
• Create a page on Bi-abduction
• Move Constrained Horn clauses to a section of Constraint logic programming
• Create C Bounded Model Checker
• Create Univalence axiom
• Add a "Motivation" section to Group representation based on the action of the dihedral group on the plane
• Add citation to the HoTT book to n-connected, rewrite and add examples. Add section on the fundamental groupoid.
• Proof irrelevance

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I'm partiularly interested in the concept of a mathematical universe. Here are some ways I'd like to improve the discussion on Wikipedia, with the goal of a complete overhaul of Universe (mathematics).

• Improve top type
• Split the "Implementation" section of top type to singly rooted hierarchy
• Do research and find out more about the top type in subtyped systems
• Add a Universes section to Calculus of Constructions. Use [http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=ABD2602A56CD9C8A82681DD4E8E4CBBA?doi=10.1.1.38.8166&rep=rep1&type=pdf this paper] or this one.
• Create Girard's Paradox (see also :Category:Mathematical paradoxes, List of paradoxes#Mathematics)
• Overhaul Universe (mathematics)
• An outline of the sections:
• Set theory
• A universal set and Russell's Paradox
• Motivation (model theory)
• Set-theoretic universes
• Von Neumann universe
• Constructible universe and Jensen Hierarchy
• Grothendieck Universe
• Category theory
• Motivation (category of categories)
• Lawvere's work: Elementary theory of the category of categories
• [http://www.mathematik.tu-darmstadt.de/~streicher/NOTES/UniTop.pdf Universes in topos theory]
• Cosmoses as a setting for category theory https://ncatlab.org/nlab/show/cosmos
• Type theory
• Motivation (dependent types)
• Motivation (formalization of mathematics)
• Universes in the Calculus of (co)Inductive Constructions
• Universes in Homotopy Type Theory

The Stanford Encyclopedia of Philosophy and Springer EOM should come in handy for the page creation aspects.

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• Create computational type theory
• Understand Preadditive category enough to add a categorical definition to Endomorphism ring
• Understand Monad (category theory) enough to improve it and add examples
• Create Algebraic category
• Merge braid theory into braid group, add the formal definition from Configuration space (mathematics)
• Distinguish and/or blend Homology (mathematics) with Chain (algebraic topology)
• Improve the "Intuition" section of Fundamental group, possibly adding figures.
• Add a section (or just a note) on the algorithmic complexity of choosing an optimal Morse function to Discrete morse theory
• Research Topological complexity to get that article to non-stub status
• Make sense of the definition of 2-group
• Explain the Common string reference model better
• Create a page on Cubical homology
• Rethink and expand the Introduction section of Homotopy group
• Improve the definition of Homotopy group, especially the spherical version (read Hatcher and Lee)
• Page on globular sets? See Awodey survey on HoTT, which has more references
• Create Homotopy n-type{{Cite web|url=https://ncatlab.org/nlab/show/homotopy+n-type|title=homotopy n-type in nLab|website=ncatlab.org|access-date=2017-09-14}}, with subsection on h-level
• Create Path space, improve Path space fibration (which assumes all spaces are compactly generated Hausdorff... in a note??)
• Add alternative definition to Natural equivalence from Topology and Groupoids{{Cite book|url=https://www.worldcat.org/oclc/712629429|title=Topology and Groupoids.|last=Ronald,|first=Brown,|date=June 2006|publisher=CreateSpace|others=Academic Search Complete.|isbn=1419627228|location=North Charleston|oclc=712629429}}
• Research and rethink the Subobject classifier

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These are not edits to articles.

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• Create a representation theory navbar, based on Template:Topology and Outline of representation theory
• Create a sidebar for finite groups. Properties: order, presentation, abelian, simple, solvable, nilpotent.
• Create a sidebar for topological spaces. Properties: (locally) connected, (locally) compact, connected components, homology groups, fundamental group, CW decomposition

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Big picture:

• Wikipedia:Maintenance
• Wikipedia:WikiProject Categories
• Wikipedia:Template messages
• Wikipedia:WikiProject Mathematics#Things to do

Important guidelines:

• Wikipedia:Tagging pages for problems#Over-tagging

• Clean up :Category:Mathematics navigational boxes.
• Add Glossary, Portal, Wikibooks and Wikiversity links to templates
• Template:Linear algebra
• Template:Group
• Add more from :Category:Mathematics templates?
• Balance content between navboxes and "outlines"

===== Stub sorting =====

• Guidelines on placement: Wikipedia:Manual of Style/Layout#Standard appendices and footers
• Edit message: Stub-sorting. You can help!
• Favorite categories:
• :Category:Computing stubs
• :Category:Software stubs
• :Category:Computer science stubs

===== Other Wikimedia resources =====

• Footer/external links templates:
• Template:Wikitionary
• Template:Wikibooks (check out the other arguments in particular)
• Template:Wikiversity
• {{EB1911 poster|{{PAGENAME}}}}

• Create a Userbox for Reed College
• Create a Userbox for NixOS

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