Picard Groups, Grothendieck Rings, and Burnside Rings of Categories

By Jon P. May. 2001

72 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8065c6aeeefcef55044d93e57488ad26cef4f02e

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Citations in the corpus

Galois equivariance and stable motivic homotopy theory (2014, background): “e equal. Proof. The identiﬁcation A(G) ∼= EndSH G(SG) is given by sending a ﬁnite G-set M to its Euler characteristic χ(M) (for a recollection of Euler characteristics and their properties see, e.g., [37]). The functor c∗ L/k is strong symmetric monoidal and so we have that c∗ L/kχ(G/H) = χ(c∗ L/k(G”
Tensor categorical foundations of algebraic geometry (2014, background): “Usually Pic(C) denotes the monoid (in fact, group) of isomorphism classes of invertible objects ([May01]), but we would like to retain the morphisms and write Pic(C)/∼= for the monoid of isomorphism classes.”
TFT construction of RCFT correlators: III: simple currents (2004, background): “ the literature there is also a diﬀerent notion of Picard group, namely the tensor subcategory consisting of all invertible objects, which is in particular a categorical group, or cat-group (see e.g. [26,27,28]). To obtain examples of pointed categories and theta-categories, we select a ﬁnite group ”
The higher Morita category of n–algebras (2014, background): “[May01] J. P.”
Parametrized homotopy theory (2004, methodology): “The equivariant analogue of the attractive space level treatment of Spanier-Whitehead duality given by Dold and Puppe was worked out in [59], and a recent categorical exposition of duality has been given in [73].”
Framed Bicategories and Monoidal Fibrations (2007, unknown): “oidal category, considered as a one-object bicategory, an adjunction in C is better known as a dual pair in C, and one speaks an object Y as being left or right dual to an object X; see, for example, [May01]. When C is symmetric monoidal, left duals and right duals coincide. Examples 6.1. When C = M”
A modular description of the K(2)-local sphere at the prime 3 (2005, background): “s of Q. Theorem 2.0.1 is ﬁnally proved in Section 2.11. 2.1 Duality pairings In this section we brieﬂy outline the abstract framework in which the duality phenomena of this paper reside. Compare with [32], [13]. We ﬁrst provide some motivation.Suppose thatVis aﬁnite dimensional vector space over a ﬁ”