Algebraic Myhill–Nerode Theorems

Algebraic proofs of some fundamental theorems in algebraic K - theory

We present new proofs of the additivity, resolution and cofinality theorems for the algebraic K-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic K-groups via binary complexes. 2000 Mathematics Subject Classification: 19D99

Basic Elements: Theorems from Algebraic Avtheory

Impossibility Theorems and the Universal Algebraic Toolkit

We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate constraint satisfaction problems. Our connection yields a full classification of non-binary evaluations into possibility and impossibility domains both under the ide...

Derived Algebraic Geometry XIV: Representability Theorems

2 Properties of Moduli Functors 22 2.1 Nilcomplete, Cohesive, and Integrable Functors . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Relativized Properties of Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Finiteness Conditions on Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 Moduli of Spectral Deligne-Mumford St...

Sum-product Theorems in Algebraic Number Fields