Abstract We provide foundations for a characteristic free study of foliated varieties in terms infinitesimal actions formal groupoids. The ultimate goal is the bi-rational geometry same, and to this end we prove cone theorem foliations curves, together with structure theorems extremal rays, and, course, minimal model surfaces. All possible wild ramification effects Deligne–Mumford champ are bui...

Abstract The variety of (pointed) residuated lattices includes a vast proportion the classes algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among outliers, one counts orthomodular and other varieties quantum algebras. We suggest ...

Homotopy Type Theory may be seen as an internal language for the ∞category of weak ∞-groupoids which in particular models the univalence axiom. Voevodsky proposes this language for weak ∞-groupoids as a new foundation for mathematics called the Univalent Foundations of Mathematics. It includes the sets as weak ∞-groupoids with contractible connected components, and thereby it includes (much of)...

744 NOTICES OF THE AMS VOLUME 43, NUMBER 7 Introduction Mathematicians tend to think of the notion of symmetry as being virtually synonymous with the theory of groups and their actions, perhaps largely because of the well-known Erlanger program of F. Klein and the related work of S. Lie, which virtually defined geometric structures by their groups of automorphisms. (See, for example, Yaglom’s a...

this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.