Timeline of Category Theory and Related Mathematics - Timeline To 1945: Before The Definitions

Timeline To 1945: Before The Definitions

Year Contributors Event
1890 David Hilbert Resolution of modules and free resolution of modules.
1890 David Hilbert Hilbert's syzygy theorem is a prototype for a concept of dimension in homological algebra.
1893 David Hilbert A fundamental theorem in algebraic geometry, the Hilbert Nullstellensatz. It was later reformulated to: the category of affine varieties over a field k is equivalent to the dual of the category of reduced finitely generated (commutative) k-algebras.
1894 Henri Poincaré Fundamental group of a topological space.
1895 Henri Poincaré Simplicial homology.
1895 Henri Poincaré Fundamental work Analysis situs, the beginning of algebraic topology.
c.1910 L. E. J. Brouwer Brouwer develops intuitionism as a contribution to foundational debate in the period roughly 1910 to 1930 on mathematics, with intuitionistic logic a by-product of an increasingly sterile discussion on formalism.
1923 Hermann Künneth Künneth formula for homology of product of spaces.
1926 Heinrich Brandt defines the notion of groupoid
1928 Arend Heyting Brouwer's intuitionistic logic made into formal mathematics, as logic in which the Heyting algebra replaces the Boolean algebra.
1929 Walther Mayer Chain complexes.
1930 Ernst Zermelo–Abraham Fraenkel Statement of the definitive ZF-axioms of set theory, first stated in 1908 and improved upon since then.
c.1930 Emmy Noether Module theory is developed by Noether and her students, and algebraic topology starts to be properly founded in abstract algebra rather than by ad hoc arguments.
1932 Eduard Čech Čech cohomology, homotopy groups of a topological space.
1933 Solomon Lefschetz Singular homology of topological spaces.
1934 Reinhold Baer Ext groups, Ext functor (for abelian groups and with different notation).
1935 Witold Hurewicz Higher homotopy groups of a topological space.
1936 Marshall Stone Stone representation theorem for Boolean algebras initiates various Stone dualities.
1937 Richard Brauer–Cecil Nesbitt Frobenius algebras.
1938 Hassler Whitney "Modern" definition of cohomology, summarizing the work since James Alexander and Andrey Kolmogorov first defined cochains.
1940 Reinhold Baer Injective modules.
1940 Kurt Gödel–Paul Bernays Proper classes in set theory.
1940 Heinz Hopf Hopf algebras.
1941 Witold Hurewicz First fundamental theorem of homological algebra: Given a short exact sequence of spaces there exist a connecting homomorphism such that the long sequence of cohomology groups of the spaces is exact.
1942 Samuel Eilenberg–Saunders Mac Lane Universal coefficient theorem for Čech cohomology; later this became the general universal coefficient theorem. The notations Hom and Ext first appear in their paper.
1943 Norman Steenrod Homology with local coefficients.
1943 Israel Gelfand–Mark Naimark Gelfand–Naimark theorem (sometimes called Gelfand isomorphism theorem): The category Haus of locally compact Hausdorff spaces with continuous proper maps as morphisms is equivalent to the category C*Alg of commutative C*-algebras with proper *-homomorphisms as morphisms.
1944 Garrett Birkhoff–Øystein Ore Galois connections generalizing the Galois correspondence: a pair of adjoint functors between two categories that arise from partially ordered sets (in modern formulation).
1944 Samuel Eilenberg "Modern" definition of singular homology and singular cohomology.
1945 Beno Eckmann Defines the cohomology ring building on Heinz Hopf's work.

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