TL;DR
This paper generalizes the computation of weighted colimits from 1-categories to 2-categories, providing a method to compute weighted pseudo-colimits and bicolimits of category-valued pseudo-functors.
Contribution
It introduces a new construction for weighted pseudo-colimits in 2-categories, extending classical results from SGA4 to higher categorical contexts.
Findings
Provides a method to compute weighted pseudo-colimits in 2-categories
Derives a way to compute weighted bicolimits from the pseudo-colimit construction
Extends classical colimit computation techniques to higher categories
Abstract
A well-known result of SGA4 shows how to compute the pseudo-colimit of a category-valued pseudo-functor on a 1-category. The main result of this paper gives a generalization of this computation by constructing the weighted pseudo-colimit of a category-valued pseudo-functor on a 2-category. From this is derived a computation of the weighed bicolimit of a category-valued pseudo-functor.
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Taxonomy
TopicsPolynomial and algebraic computation · Computability, Logic, AI Algorithms · Logic, programming, and type systems