Categories for the Working Mathematician

By S. Lane. 1971

Subfields: Automated Theorem Proving & Formal Methods

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In Automated Theorem Proving & Formal Methods

1. V. Drinfeld
2. B. Shipley
3. F. Digne
4. D. Tambara
5. Thomas H. Geisser
6. Trent Yeend
7. Kathleen Ponto
8. Wendy Lowen

Citations in the corpus

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• Notes on Grothendieck topologies, fibered categories and descent theory (2004, background): “ finite presentation. 1.0.2. Category theory. We will assume that the reader is familiar with the concepts of category, functor and natural transformation. The standard reference in category theory is [25]; also very useful are [6], [7] and [8]. We will not distinguish between small and large categor”
• Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces (2004, background): “We assume the reader is familiar with both of these notions (see [5]) as well as with their one object versions, the strict and weak monoidal categories (see [24], [26]).”
• Quantum link homology via trace functor I (2016, background): “ects (x,y,z), and • natural isomorphisms a: f◦(g◦h) ∼= (f◦g)◦h l: idy ◦f ∼= f r: f◦idx ∼= f (A.1) called associators and unitors, which satisfy the pentagon and triangle axioms of a monoidal category [ML98]. 56 A bicategory is called strict or a 2–category if the natural isomorphisms are identities.”
• On equivariant homotopy theory for model categories (2013, background): “ctor but along a set of left adjoints from Cto D. The reader is assumed to have some basic knowledge of algebraic topology and category theory such as treated for instance in [19] and Mac Lane’s book [14], respectively. Properties of compactly generated spaces are listed in A. The for this paper nec”
• Cofibrations in Homotopy Theory (2006, background): “a) u1 (resp. u2) is fully faithful iff φ(resp. ψ) is a natural isomorphism. (b) u1 and u2 are inverse equivalences of categories iff both φand ψare natural isomorphisms. Proof. See for example Mac Lane [Lan98]. Here is another way to state part (2) of the previous proposition. The proof is left to the”
• MORITA EQUIVALENCE OF SEMIGROUPS WITH LOCAL UNITS (2009, background): “1 of [15], there is a left S-homomorphism given by”