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Barcelona Algebraic Topology Group
Friday's Topology Seminar 2018-19 PDF Print E-mail
Written by Natàlia Castellana Vila   
Friday, 30 November 2018 14:12

Speaker: Philip Hackney
Title:
Right adjoints to operadic restriction functors
Place:
Room Seminar C3b
Date: Friday July 18th, 9:45-10:45

Abstract: If f : P → Q is a morphism of operads, then there is a restriction functor from Q-algebras to P-algebras. This restriction functor generally admits a left adjoint. This restriction may or may not admit a right adjoint: if G → H is a group homomorphism, then the forgetful functor from H-sets to G-sets has a right adjoint, while there is no right adjoint to the functor from commutative algebras to associative algebras. In this talk, we provide a concise necessary and sufficient condition for the existence of a right adjoint to the restriction functor, phrased in terms of the operad map f. We give a simple formula for this right adjoint, and examine the criterion in special cases. All of this is applicable over quite general ground categories. (Joint work with Gabriel C. Drummond-Cole)

 

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Last Updated on Thursday, 18 July 2019 08:31
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This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR-42 and Homotopy theory of algebraic structures, MTM2016-80439-P).

Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities.

 

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