NDLI: Contractible Exact Squares

Content Provider	Springer Nature Link
Author	Guitart, René
Copyright Year	2013
Abstract	Exact squares in Cat are not necessarily absolute (i.e., preserved by any 2-functor Cat → Cat), or even preserved by any 2-functor given by exponentiation (−)ℐ : Cat → Cat: if a square is preserved by exponentiation it will be called a contractible exact square. We will characterize diagrammatically these contractible squares, and among them the contractible categories, and the so called fibering and cofibering squares, with especially the comma squares and the adjunction squares. As an application we conclude with a diagrammatical characterization of absolutely absolute Kan extensions and especially of absolutely final functors and of absolutely absolute colimits.
Starting Page	873
Ending Page	898
Page Count	26
File Format	PDF
ISSN	09272852
Journal	Applied Categorical Structures
Volume Number	22
Issue Number	5-6
e-ISSN	15729095
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-12-05
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Exact squares Distributors Contractible spaces Fibrations Mathematical Logic and Foundations Theory of Computation Convex and Discrete Geometry Geometry
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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Contractible Exact Squares