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Effective Kan Fibrations in Simplicial Sets
Engelsk
Bogcover for Effective Kan Fibrations in Simplicial Sets af Eric Faber, Benno van den Berg, 9783031188992
Specifikationer
Sprog:
Engelsk
Sider:
230
ISBN-13:
9783031188992
Indbinding:
Paperback
ISBN-10:
3031188993
Udg. Dato:
10 dec 2022
Størrelse i cm:
23,5 x 15,5
Oplagsdato:
10 dec 2022

Effective Kan Fibrations in Simplicial Sets

Engelsk
Paperback 2022
Format:

Bog beskrivelse
This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodsky''s model of univalent type theory in simplicial sets.
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Specifikationer
Sprog:
Engelsk
Sider:
230
ISBN-13:
9783031188992
Indbinding:
Paperback
ISBN-10:
3031188993
Udg. Dato:
10 dec 2022
Størrelse i cm:
23,5 x 15,5
Oplagsdato:
10 dec 2022
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