Holmstrom Algebraic category

nLab “essentially algebraic theory”

nLab on algebraic theory

http://mathoverflow.net/questions/3003/in-what-sense-are-fields-an-algebraic-theory

See also Barr-Beck thm or something like that

Schwede has some notions for triangulated cats I think

Boerceaux vol 2 page 158: A cat equipped with a functor U to sets is called algebraic if (a) it has coequalizers and kernel pairs (b) U has a left adjoint F (c) U reflects isomorphisms (d) U preserves regular epimorphisms (e) UF preserves filtered colimits.

http://mathoverflow.net/questions/49784/the-z-2-cohomology-functor-from-top-to-grvecspaces-factors-through-unstable-a-mo

arXiv:1109.1598 Algebraic theories, span diagrams and commutative monoids in homotopy theory from arXiv Front: math.CT by James Cranch We adapt the notion of an algebraic theory to work in the setting of quasicategories developed recently by Joyal and Lurie. We develop the general theory at some length

We study one extended example in detail: the theory of commutative monoids (which turns out to be essentially just a 2-category). This gives a straightforward, combinatorially explicit, and instructive notion of a commutative monoid. We prove that this definition is equivalent (in appropriate senses) both to the classical concept of an E-infinity monoid and to Lurie’s concept of a commutative algebra object.

nLab page on Algebraic category

Created on June 9, 2014 at 21:16:13 by Andreas Holmström