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.
Bonchi F., Sobocinski P., Zanasi F. (2016). Lawvere categories as composed PROPs. GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND : SPRINGER INTERNATIONAL PUBLISHING AG [10.1007/978-3-319-40370-0_3].
Lawvere categories as composed PROPs
Zanasi F.
2016
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
