In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...
We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...
We apply the Acyclicity Theorem of Hess, Kedziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from simplicial adjuncti ...
This thesis is part of a program initiated by Riehl and Verity to study the category theory of (infinity,1)-categories in a model-independent way. They showed that most models of (infinity,1)-categories form an infinity-cosmos K, which is essentially a cat ...
A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalence ...
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes ...
We prove existence results à la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation fro ...
We analyze the renormalon diagram of gauge theories on . In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel be ...
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 ...
We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base catego ...
