no code implementations • 11 Jul 2018 • J. Daniel Christensen, Morgan Opie, Egbert Rijke, Luis Scoccola
Our main result is that for a pointed, simply connected type $X$, the natural map $X \to X_{(p)}$ induces algebraic localizations on all homotopy groups.
Algebraic Topology Category Theory 55P60 (Primary), 18E35, 03B15 (Secondary)
1 code implementation • 12 Feb 2018 • Ulrik Buchholtz, Floris van Doorn, Egbert Rijke
We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type theory.
Logic in Computer Science Algebraic Topology Logic 03B15 F.4.1
1 code implementation • 19 Apr 2017 • Ulrik Buchholtz, Egbert Rijke
In the inductive step, we take RP(n+1) to be the mapping cone of the projection map of the tautological bundle of RP(n), and we use its universal property and the univalence axiom to define the tautological bundle on RP(n+1).
Algebraic Topology 03B15, 55P20, 55U35
no code implementations • 26 Jan 2017 • Egbert Rijke
In homotopy type theory we can define the join of maps as a binary operation on maps with a common co-domain.
Category Theory Logic
no code implementations • 4 Oct 2016 • Ulrik Buchholtz, Egbert Rijke
We define in the setting of homotopy type theory an H-space structure on $\mathbb S^3$.
Algebraic Topology Logic in Computer Science Category Theory Logic 03B15, 17A35, 55P45, 55U35
