Weakly Distributive Categories

Weakly Distributive Categories (1991)

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by Cockett Seely , J. R. B. Cockett , R. A. G. Seely

Venue:	Journal of Pure and Applied Algebra
Citations:	102 - 18 self

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Datum	Value	Source
TITLE	Weakly Distributive Categories	user correction - Legacy Corrections
AUTHOR NAME	Cockett Seely	user correction - Legacy Corrections
AUTHOR NAME	J. R. B. Cockett	user correction - Legacy Corrections
AUTHOR NAME	R. A. G. Seely	user correction - Legacy Corrections
ABSTRACT	There are many situations in logic, theoretical computer science, and category theory where two binary operations---one thought of as a (tensor) "product", the other a "sum"---play a key role. In distributive and -autonomous categories these operations can be regarded as, respectively, the and/or of traditional logic and the times/par of (multiplicative) linear logic. In the latter logic, however, the distributivity of product over sum is conspicuously absent: this paper studies a "linearization" of that distributivity which is present in both case. Furthermore, we show that this weak distributivity is precisely what is needed to model Gentzen's cut rule (in the absence of other structural rules) and can be strengthened in a natural way to generate - autonomous categories. We also point out that this "linear" notion of distributivity is virtually orthogonal to the usual notion as formalized by distributive categories. 0 Introduction There are many situations in logic, theoretical co...	user correction - Legacy Corrections
YEAR	1991	user correction - Legacy Corrections
VENUE	Journal of Pure and Applied Algebra	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	45--65	INFERENCE
VOLUME	114	INFERENCE
CITATIONS	15 found	ParsCit 1.0