Abstract : 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.
https://hal.inria.fr/hal-01446031 Contributor : Hal IfipConnect in order to contact the contributor Submitted on : Wednesday, January 25, 2017 - 3:24:22 PM Last modification on : Saturday, September 11, 2021 - 3:18:33 AM Long-term archiving on: : Wednesday, April 26, 2017 - 3:07:07 PM