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Full-Text Articles in Logic and Foundations
Category Theory And Universal Property, Niuniu Zhang
Category Theory And Universal Property, Niuniu Zhang
Honors Theses
Category theory unifies and formalizes the mathematical structure and concepts in a way that various areas of interest can be connected. For example, many have learned about the sets and its functions, the vector spaces and its linear transformation, and the group theories and its group homomorphism. Not to mention the similarity of structure in topological spaces, as the continuous function is its mapping. In sum, category theory represents the abstractions of other mathematical concepts. Hence, one could use category theory as a new language to define and simplify the existing mathematical concepts as the universal properties. The goal of …
Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz
Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz
Engineering Faculty Articles and Research
This report documents the program and the outcomes of Dagstuhl Seminar 12411 “Coalgebraic Logics”. The seminar deals with recent developments in the area of coalgebraic logic, a branch of logics which combines modal logics with coalgebraic semantics. Modal logic finds its uses when reasoning about behavioural and temporal properties of computation and communication, coalgebras have evolved into a general theory of systems. Consequently, it is natural to combine both areas for a mathematical description of system specification. Coalgebraic logics are closely related to the broader categories semantics/formal methods and verification/logic.