This book develops abstract homotopy theory from the categorical perspective with a
particular focus on examples. Part I discusses two competing perspectives by which one …

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 …

This paper defines double fibrations (fibrations of double categories) and describes their key
examples and properties. In particular, it shows how double fibrations relate to existing …

In Part I of this thesis, we introduce algebraic model structures, a new context for homotopy
theory in which the cofibrations and fibrations are retracts of coalgebras for comonads and …

We present a method of constructing monoidal, braided monoidal, and symmetric monoidal
bicategories from corresponding types of monoidal double categories that satisfy a lifting …

Via the adjunction-∗ 1⊣ V (1,-): Span (V)→ V-Mat and a cartesian monad T on an extensive
category V with finite limits, we construct an adjunction-∗ 1⊣ V (1,-): Cat (T, V)→(T¯, V)-Cat …

Motivated by traces of matrices and Euler characteristics of topological spaces, we expect
abstract traces in a symmetric monoidal category to be “additive”. When the category is …

The category of double categories and double functors is equipped with a symmetric closed
monoidal structure. For any double category AA, the corresponding internal hom functor …

This article compares the infinite loop spaces associated to symmetric spectra, orthogonal
spectra and EKMM S–modules. Each of these categories of structured spectra has a …

By the Lefschetz fixed point theorem, if an endomorphism of a topological space is fixed-
point-free, then its Lefschetz number vanishes. This necessary condition is not usually …