All of these are used heavily in computer science as abstractions for modelling dynamical systems. * Monoidal categories give models of linear and other substructural logics, which have proof-theoretic readings in terms of state change. * Sheaves arise as categorifications of Kripke models. By considering the internal set theory of sheaf categories, we can extend traditional Kripke models to talk about (say) variable sets, and not merely variable propositions. * Coalgebra let us model systems in terms of their observable behavior – a class of behaviors is described by the final coalgebra for a functor F, and a particular system is a (non-final) coalgebra for this functor c:A→F(A). We can equate two systems c:A→F(A) and d:B→F(B) just when they are bisimilar.
![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
no subject
Date: 2012-09-25 04:16 pm (UTC)All of these are used heavily in computer science as abstractions for modelling dynamical systems.
* Monoidal categories give models of linear and other substructural logics, which have proof-theoretic readings in terms of state change.
* Sheaves arise as categorifications of Kripke models. By considering the internal set theory of sheaf categories, we can extend traditional Kripke models to talk about (say) variable sets, and not merely variable propositions.
* Coalgebra let us model systems in terms of their observable behavior – a class of behaviors is described by the final coalgebra for a functor F, and a particular system is a (non-final) coalgebra for this functor c:A→F(A). We can equate two systems c:A→F(A) and d:B→F(B) just when they are bisimilar.