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2 results

Nilpotent types and fracture squares in homotopy type theory
Luis Scoccola
Journal:

Mathematical Structures in Computer Science / Volume 30 / Issue 5 / May 2020

Published online by Cambridge University Press:

08 July 2020, pp. 511-544
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We develop the basic theory of nilpotent types and their localizations away from sets of numbers in Homotopy Type Theory. For this, general results about the classifying spaces of fibrations with fiber an Eilenberg–Mac Lane space are proven. We also construct fracture squares for localizations away from sets of numbers. All of our proofs are constructive.

Extension of Maps to Nilpotent Spaces
M. Cencelj, A. N. Dranishnikov
Journal:

Canadian Mathematical Bulletin / Volume 44 / Issue 3 / 01 September 2001

Published online by Cambridge University Press:

20 November 2018, pp. 266-269

Print publication:

01 September 2001
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We show that every compactum has cohomological dimension 1 with respect to a finitely generated nilpotent group $G$ whenever it has cohomological dimension 1 with respect to the abelianization of $G$. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum $X$ for extendability of every map from a closed subset of $X$ into a nilpotent $\text{CW}$-complex $M$ with finitely generated homotopy groups over all of $X$.