Cocompletion of restriction categories
Richard Garner, Daniel Lin
TL;DR
This paper introduces the concept of cocomplete restriction categories, providing a construction for their free cocompletion via restriction presheaves, and explores the case of locally small restriction categories.
Contribution
It defines cocomplete restriction categories and constructs their free cocompletion, extending the theory of restriction categories with new categorical tools.
Findings
Defined cocomplete restriction categories
Constructed free cocompletion via restriction presheaves
Analyzed locally small restriction categories
Abstract
Restriction categories were introduced as a way of generalising the notion of partial map categories. In this paper, we define cocomplete restriction category, and give the free cocompletion of a small restriction category as a suitably defined category of restriction presheaves. We also consider the case where our restriction category is locally small.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Intracranial Aneurysms: Treatment and Complications