PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category, but whereas PROPs are symmetric monoidal, Lawvere categories are cartesian. This paper formulates the connection between the two notions using Lack’s technique for composing PROPs via distributive laws. We show Lawvere categories can be seen as resulting from a distributive law of two PROPs — one expressing the algebraic structure in linear form and the other expressing the ability of copying and discarding variables.
CITATION STYLE
Bonchi, F., Sobocinski, P., & Zanasi, F. (2016). Lawvere categories as composed PROPs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9608, pp. 11–32). Springer Verlag. https://doi.org/10.1007/978-3-319-40370-0_3
Mendeley helps you to discover research relevant for your work.