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Mike Shulman

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I am currently a member of the Institute for Advanced Study, participating in the special year on univalent foundations and homotopy type theory. Starting in Fall 2013, I will be an Assistant Professor at the University of San Diego. Here is my web page.

Research-wise, I am interested in (higher) category theory and its applications to the rest of mathematics, particularly homotopy theory. I also tend to be a partisan of higher-categorical structures other than n-categories (such as double categories, multicategories, proarrow equipments, F-categories, and so on), which sometimes seem to get neglected.

Personal area

For my own reference: some pages that I’m planning to do some work on:

And here’s how to make a barred arrow A⇸B, since I always forget:

  ⇸

category: people

Revised on September 24, 2012 18:56:37 by Mike Shulman (192.16.204.218)
Edit | Back in time (39 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: horizontal categorification, groupoid, vertical categorification, fundamental groupoid, 2009 June changes, well-pointed topos, double category, quasi-category, nonabelian cohomology, principle of equivalence, (n,r)-category, n-category, virtual double category, k-tuply monoidal n-category, nice topological space, discussion on terminology -- omega-category, Contributors, geometric morphism, tricategory, coherent category, Grothendieck fibration, context, hyperstructure, trace, dualizable object, profunctor, 2009 January changes, classifying space, comma object, homotopy pullback, Euler characteristic, n-fibration, weighted limit, 2009 February changes, homotopy group, fundamental group, compactly generated topological space, Postnikov system, homotopy equivalence, profinite completion of a group, predicative mathematics, symmetric set, fundamental group of a topos, cyclic set, cycle category, finitary monad, Grothendieck universe, finite category, universe in a topos, idempotent monad, bimorphism, biproduct, derived functor on a derived category, sheafification, 2009 March changes, semi-abelian category, cohomology, combinatorial spectrum, inaccessible cardinal, type theory, minimal logic, well-ordering theorem, cyclic order, k-simply connected n-category, 2009 April changes, lax 2-adjunction, anabicategory, simplicial model for weak omega-categories, flat functor, pseudotopological space, higher category theory and physics, 2009 May changes, gauge space, replete subcategory, weighted colimit, lax natural transformation, group cohomology, transfor, Lectures on n-Categories and Cohomology, 2009 July changes, Karoubi K-theory, locally cartesian category, lax functor, generalized multicategory, 2009 August changes, Cartesian morphism, Benabou-Roubaud theorem, monotone function, monadic adjunction, 2-category equipped with proarrows, affine space, graph, 2009 September changes, Charles Sanders Peirce, equivariant cohomology, derivator, graph of a functor, natural numbers in SEAR, choice operator, fibration of bigroupoids, SEAR plus epsilon, multiset, ZFC, universes in SEAR, completion, Ho(Cat), regular and exact completions, natural transformation (discussion), endomorphism operad, ionad, elementary embedding, framed bicategory, category of operators, codomain fibration, category over a category, small violations of choice, inhabited object, Grothendieck-Maltsiniotis infinity-category, Thom spectrum, axiom of multiple choice, virtual equipment, 2-topos, club, tileorder, reflective sub-(infinity,1)-category, monoidal bicategory, enriched derivator, W-type, coherence theorem, transferred model structure, algebrad, compact double category, integer, discrete morphism, doctrinal adjunction, geometric homotopy groups in an (infinity,1)-topos, homotopy equivalence of toposes, adjoint monad, monoidal fibration, cohesive (infinity,1)-topos, uniform locale, local geometric morphism, circle, (infinity,1)-quasitopos, bicategory of maps, vDbl, Leinster2010, two-sided fibration, geometric category, 2-type theory, 2-logic, categorical semantics, historical note on Grothendieck topology, homotopy type theory, small cardinality selection axiom, F-category, concrete object, stack semantics, cohesive homotopy type theory, bicategorical trace, stable factorization system, rigged limit, interval type, bracket type, higher gauge field, inductive type, higher inductive type, univalence axiom, type-theoretic model category, reflective sub-(infinity,1)-category - internal formulation, codiscrete object, co-concrete object, equivalence in homotopy type theory, StreetCBS, Sierpinski topos, 2-Giraud theorem, 2-pretopos, extensive 2-category, (n,r)-congruence, 2-congruence, initial algebra of a presentable (infinity,1)-monad, elementary (infinity,1)-topos, relation between type theory and category theory, pretopos completion, general covariance, indexed monoidal category, separator, modal type theory, symmetric monoidal 2-category, core in a 2-category, n-localic 2-topos