NDLI: Absolute Lax 2-categories

Content Provider	Springer Nature Link
Author	Grandis, Marco
Copyright Year	2006
Abstract	We have introduced, in a previous paper, the fundamental lax 2-category of a ‘directed space’ $X$ . Here we show that, when $ X $ has a $T_1$ -topology, this structure can be embedded into a larger one, with the same objects (the points of $ X$ ), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells are absolute, in the sense that they only depend on the arrows themselves rather than on their syntactic expression, as in the usual settings of lax or weak structures. It follows that, in the original structure, all the diagrams of comparison cells commute, even if not constructed in a natural way and even if the composed cells need not stay within the old system.
Ending Page	214
Page Count	24
Starting Page	191
File Format	PDF
ISSN	09272852
e-ISSN	15729095
Journal	Applied Categorical Structures
Issue Number	3
Volume Number	14
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-07-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	homotopy theory Geometry Homotopy theory lax 2-categories bicategories Convex and Discrete Geometry directed algebraic topology Theory of Computation 2-categories fundamental categories Double categories, $2$ -categories, bicategories and generalizations Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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