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We generalize Cohen & Jones & Segal's flow category, whose objects are the critical points of a Morse function and whose morphisms are the Morse moduli spaces between the critical points to an n-category. The n-category construction involves repeatedly doi ...
We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...
Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...
Being void-free is an important criterion for the quality control of photovoltaic (PV) modules after encapsulation. The encapsulation process of PV modules with Ethylene Vinyl Acetate (EVA) polymer is complex, due to the time-dependent processing condition ...
Kan spectra provide a combinatorial model for the stable homotopy category. They were introduced by Dan Kan in 1963 under the name semisimplicial spectra. A Kan spectrum is similar to a pointed simplicial set, but it has simplices in negative degrees as we ...
We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a growth condition implies a structure theorem and that mo ...
This thesis is in the context of representation theory of finite groups. More specifically, it studies biset functors. In this thesis, I focus on two biset functors: the Burnside functor and the functor of p-permutation modules. For the Burnside functor we ...
Bacterial species take on a wide variety of shapes, but the mechanisms by which specific shapes evolve have remained poorly understood. A recent study demonstrates that two Asticcacaulis species repurposed an ancestral regulatory protein to rewire the modu ...
We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisel ...
The category of “creative city” is far from neutral. Indeed, it can be linked to very contrasted – and even opposed – practices and urban worlds. In order to grasp those differences, we need to take a closer look at what is entailed in the concepts of “cre ...