Problem
Research questions and friction points this paper is trying to address.
override
update
restriction categories
partial functions
Override and Update in Restriction Categories
๐ค AI Summary
็ ็ฉถไบไป้ๅถ่็ด่งๅบฆๅค็ๅๅฝๆฐ็่ฆ็ๅๆดๆฐๆไฝ๏ผๅฎไนไบ่ฆ็้ๅถ่็ดๅนถ่ฏๆไบ็ธๅ
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๐ Abstract
We study the override and update operators on partial functions from the perspective of restriction categories. We propose a definition of override restriction categories, in which both of the operators in question exist. We prove a number of results concerning these operators and their relationship to the structure of the ambient restriction category, as well as relating them to the existing literature on the override and update operators. We provide various examples of override restriction categories and in particular show that every classical restriction category is an override restriction category.
Innovation
Methods, ideas, or system contributions that make the work stand out.
override restriction categories
update operators
partial functions
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