Categories of (co)isotropic linear relations

Two Categories of Relations

Categories of Relations and Functional Relations

Relations in Categories

This thesis investigates relations over a category C relative to an (E;M)-factorization system of C. In order to establish the 2-categoryRel(C) of relations over C in the rst part we discuss su cient conditions for the associativity of horizontal composition of relations, and we investigate special classes of morphisms in Rel(C). Attention is particularly devoted to the notion of mapping as de ...

Categories of Timed Stochastic Relations

Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior...

Dagger Categories of Tame Relations

Within the context of an involutive monoidal category the notion of a comparison relation cp : X ⊗X → Ω is identified. Instances are equality = on sets, inequality ≤ on posets, orthogonality ⊥ on orthomodular lattices, non-empty intersection on powersets, and inner product 〈− |−〉 on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category...