Andrè-Quillen Cohomology and the k-Invariants of Simplicial Categories

Abstract: Spaces, and more generally infinity-categories, have a canonical decomposition into simpler pieces known as Postnikov sections, which are glued together by their k-invariants. For an $\infty$-category X, these take value in the spectral Andre-Quillen cohomology of Harpaz, Nuiten, and Prasma. By pulling these k-invariants back to diagrams inside X, one obtains a series of obstructions to lifting the diagram to successive stages in the Postnikov tower.

In this talk, we will show how various constructions in algebraic topology, such as differentials in spectral sequences and cohomology operations, can be viewed as obstructions to extending cubical diagrams in the infinity category of spaces. Motivated by this, we will also show that there exists a canonical cubical decomposition of the spectral Andre-Quillen cohomology. Joint work with David Blanc.

commutative algebraalgebraic geometryalgebraic topologycategory theorygeometric topologyK-theory and homology

Audience: researchers in the topic

Comments: Join Zoom Meeting unipv-it.zoom.us/j/94344875868

Meeting ID: 943 4487 5868

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Transalpine Topology Tetrahedron (TTT) - Pavia Vertex

Series comments: The Transalpine Topology Tetrahedron (TTT) is a topology seminar partially supported by the London Mathematical Society (LMS) and INdAM. It has UK nodes at Liverpool, Sheffield and Warwick and an international node at Pavia. For many years TTT stood for Transpennine Topology Triangle.

Website: sarah-whitehouse.sites.sheffield.ac.uk/transalpine-topology-tetrahedron

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