
Higher Groups in Homotopy Type Theory
We present a development of the theory of higher groups, including infin...
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Analysis of Cellular Feature Differences of Astrocytomas with Distinct Mutational Profiles Using Digitized Histopathology Images
Cellular phenotypic features derived from histopathology images are the ...
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Integrality of matrices, finiteness of matrix semigroups, and dynamics of linear cellular automata
Let K be a finite commutative ring, and let L be a commutative Kalgebra...
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Cell Complex Neural Networks
Cell complexes are topological spaces constructed from simple blocks cal...
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Latin Hypercubes and Cellular Automata
Latin squares and hypercubes are combinatorial designs with several appl...
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Addendum to "Tilings problems on BaumslagSolitar groups"
In our article in MCU'2013 we state the the Domino problem is undecidabl...
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Cooperation in Small Groups – an Optimal Transport Approach
If agents cooperate only within small groups of some bounded sizes, is t...
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Cellular Cohomology in Homotopy Type Theory
We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian groups of many common spaces are easier to compute in many cases. Cellular cohomology is a special kind of cohomology designed for cell complexes: these are built in stages by attaching spheres of progressively higher dimension, and cellular cohomology defines the groups out of the combinatorial description of how spheres are attached. Our main result is that for finite cell complexes, a wide class of cohomology theories (including the ones defined through EilenbergMacLane spaces) can be calculated via cellular cohomology. This result was formalized in the Agda proof assistant.
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