The category of uniform frames
The category of uniform spaces as a completion of the category of metric spaces
A criterion for the existence of an initial completion of a concrete category universal w.r.tḟinite products and subobjects is presented. For metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
The catgorical theory of self-similarity.
The Chinese remainder theorem and sheaf representations
The Chu construction.
The Chu construction: history of an idea.
The classifying space of the 1 + 1 dimensional cobordism category.
The classifying topos of a continuous groupoid. II
The closure of a model category
The cohomological dimension of the ordered set of real numbers equals three
The Cohomology Ring of a Monomial Algebra.
The colimits in the generalized algebraic categories
The commuting of coreflectors in uniform spaces with completion
The completion monad and its algebra
The complex of words and Nakaoka stability.
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 concept of a binary relation over partial enumerated sets.
The connection between May's axioms for a triangulated tensor product and Happel's description of the derived category of the quiver .
The connection between the fundamental groupoid and a unification algorithm for syntactil algebras (extended abstract)