The catgorical theory of self-similarity.
The Chu construction.
The Chu construction: history of an idea.
The classifying topos of a continuous groupoid. II
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
The convergence approach to exponentiable maps.
The existence and construction of Lax limits
The extensive completion of a distributive category.
The free adjunction
The Frobenius relations meet linear distributivity.
The fundamental groupoid scheme and applications
We define a linear structure on Grothendieck’s arithmetic fundamental group of a scheme defined over a field of characteristic 0. It allows us to link the existence of sections of the Galois group to with the existence of a neutral fiber functor on the category which linearizes it. We apply the construction to affine curves and neutral fiber functors coming from a tangent vector at a rational point at infinity, in order to follow this rational point in the universal covering of the affine...
The Heyting doctrines
The Hurwitz action and braid group orderings.
The infinite minimal rich monoid
The Khovanov-Lauda 2-category and categorifications of a level two quantum representation.
The low-dimensional homology of crossed modules.
The maximality of the typed lambda calculus and of cartesian closed categories
The monoidal centre as a limit.
The natural number bialgebra