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2 results

  • 2 - Algebras and Coalgebras

  • Jiří Adámek, Czech Technical University in Prague, Stefan Milius, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, Lawrence S. Moss, Indiana University, Bloomington
  • Book:
    Initial Algebras and Terminal Coalgebras
    Published online:
    30 January 2025
    Print publication:
    06 February 2025, pp 12-64

  • Summary

    This chapter provides examples of the central concepts of the book: initial algebras and terminal coalgebras. These are mainly for polynomial endofunctors on the category of sets, but also for such functors on sorted sets, nominal sets, and presheaves. We discuss connections to induction and recursion and to their duals, coinduction and corecursion, and also to bisimulation. We present Lambek’s Lemma, a result used throughout the book.

  • KRS and Powers of determinantal ideas

  • WINFRIED BRUNS, ALDO CONCA
  • Journal:
    Compositio Mathematica / Volume 111 / Issue 1 / March 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 111-122
    Print publication:
    March 1998
    • Article
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  • The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.