PlanetPhysics/Axiomatic Theories and Categorical Foundations of Mathematics

This is a contributed topic entry on the axiomatic foundations of mathematics.

Axiomatic Theories and Categorical Foundations of Mathematical Physics and Mathematics
and so on)
 * 1) Axiomatic foundations of adjointness, equivalence relations, isomorphism and abstract mathematics
 * 2) Syntax, semantics and structures
 * 3) Axioms of set theory and theories of classes
 * 4) Axiomatics and logics
 * 5) Axioms of logic algebras and lattices: Post, \htmladdnormallink{\L{}ukasiewicz}{http://planetphysics.us/encyclopedia/AlgebraicCategoryOfLMnLogicAlgebras.html} and $$MV$$ logics
 * 6) Axioms of algebraic topology and algebraic geometry
 * 7) Axioms of abstract and universal algebras
 * 8) Abstract Relational Theories, algebraic systems and relational structures
 * 9) Axioms of homological algebra
 * 10) Axioms of ETAC and category theory
 * 11) Axioms of 2-categories and n-categories #Axioms of Abelian structures and theories
 * 12) Axioms of Abelian categories ($$Ab1$$ to $$Ab6$$, incl. $$*$$ axioms)
 * 13) Categories of logic algebras
 * 14) functor categories and super-categories
 * 15) index of category theory #axioms of topoi and extended toposes
 * 16) Axioms of ETAS, supercategories and higher dimensional algebra #Axioms for non-Abelian structures and theories
 * 17) Axioms of non-Abelian algebraic topology
 * 18) Axioms of algebraic quantum field theories
 * 19) Topic entry on real numbers
 * 20) Classical and categorical Galois theories
 * 21) Axioms of model theory
 * 22) Axioms for symbolic and categorical computations #Axioms of measure theory
 * 23) Axioms of representation theory (e.g., algebra, group, groupoid representations,


 * 1) new contributed additions

Note The following page is only a short list of relevant papers. A more substantial bibliography is now being compiled separately.

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