Categories and all that -- A Tutorial
Logic in Computer Science
2014-10-09 v2
Abstract
This is a short introduction to categories with some emphasis on coalgebras. We start from introducing basic notions (categories, functors, natural transformations), move to Kleisli tripels and monads, with a short discussion of monads in Haskell, and continue with displaying the interplay between algebras, adjunctions and monads. Coalgebras are discussed and applied to the semantics of modal logics, giving a brief introduction to coalgebraic logics as well. The development is illustrated through examples, usually taken from applications to computer science, with a certain predilection for stochastic systems.
Keywords
Cite
@article{arxiv.1403.7760,
title = {Categories and all that -- A Tutorial},
author = {Ernst-Erich Doberkat},
journal= {arXiv preprint arXiv:1403.7760},
year = {2014}
}