From Objects to Diagrams for Ranges of Functors [electronic resource] /
Gillibert, Pierre.author.
Wehrung, Friedrich.author.
This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references and index.
1 Background -- 2 Boolean Algebras Scaled with Respect to a Poset -- 3 The Condensate Lifting Lemma (CLL) -- 4 Larders from First-order Structures -- 5 Congruence-Preserving Extensions -- 6 Larders from von Neumann Regular Rings -- 7 Discussion.
This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). The basic idea is: if a functor lifts many objects, then it also lifts many (poset-indexed) diagrams.
Algebra.
Category theory (Mathematics).
Homological algebra.
Ordered algebraic structures.
Mathematical logic.
K-theory.
Algebra.
Category Theory, Homological Algebra.
General Algebraic Systems.
Order, Lattices, Ordered Algebraic Structures.
Mathematical Logic and Foundations.
K-Theory.
Lecture notes in mathematics