%0 Conference Proceedings
%T Lawvere Categories as Composed PROPs
%+ Laboratoire de l'Informatique du Parallélisme (LIP)
%+ University of Southampton
%+ Radboud University [Nijmegen]
%A Bonchi, Filippo
%A Sobocinski, Pawel
%A Zanasi, Fabio
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS)
%C Eindhoven, Netherlands
%Y Ichiro Hasuo
%3 Coalgebraic Methods in Computer Science
%V LNCS-9608
%P 11-32
%8 2016-04-02
%D 2016
%R 10.1007/978-3-319-40370-0_3
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%Z TC 1
%Z WG 1.3
%2 https://inria.hal.science/hal-01446031/document
%2 https://inria.hal.science/hal-01446031/file/418352_1_En_3_Chapter.pdf
%L hal-01446031
%U https://inria.hal.science/hal-01446031
%~ ENS-LYON
%~ CNRS
%~ INRIA
%~ UNIV-LYON1
%~ LIP_PLUME
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-9608
%~ IFIP-WG1-3
%~ IFIP-CMCS
%~ INRIA-AUT
%~ UDL
%~ UNIV-LYON