Geodesic
Taut functors and the difference operator
Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 281-362.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We establish a calculus of differences for taut endofunctors of the category of sets, analogous to the classical calculus of finite differences for real valued functions. We study how the difference operator interacts with limits and colimits as categorical versions of the usual product and sum rules. The first main result is a lax chain rule which has no counterpart for mere functions. We also show that many important classes of functors (polynomials, analytic functors, reduced powers, ...) are taut, and calculate explicit formulas for their differences. Covariant Dirichlet series are introduced and studied. The second main result is a Newton summation formula expressed as an adjoint to the difference operator.
Publié le :
Classification : Primary: 18A22, 12H10, secondary: 18C15, 18F50
Keywords: Taut functor, polynomial, reduced power, analytic functor, Dirichlet series, difference operator 
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     author = {Robert Par\'e},
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Robert Paré. Taut functors and the difference operator. Theory and applications of categories, Lawvere Festschrift, Tome 43 (2025), pp. 281-362. http://geodesic.mathdoc.fr/item/TAC_2025_43_a9/