7 papers
Colimits in Oriented Category Theory
David Gepner, Hadrian Heine
In higher category theory, lax colimits are often understood to be a more useful and powerful generalization of usual (homotopy) colimits, which can be recovered from the lax colim…
Fibrations in Oriented Category Theory
David Gepner, Hadrian Heine
We study fibrations of higher categories from the perspective of oriented category theory, a framework which accounts for lax phenomena in higher category theory via systematic enr…
An Oriented Street--Roberts Conjecture
David Gepner, Hadrian Heine
We formulate a notion of oriented polytope, including Street's oriented simplices and Gray's oriented cubes, and use this to prove an oriented version of the Street--Roberts conjec…
Oriented Category Theory
David Gepner, Hadrian Heine
As categorical dimension increases, classical categorical concepts often become too rigid and must be replaced by appropriately lax analogues. A basic manifestation of this princip…
Homology of higher categories
Hadrian Heine
Homology is characterized by the Eilenberg-Steenrod axioms. We define homology of higher categories via a categorical analogue of the Eilenberg-Steenrod axioms. We prove a categori…
Stable homotopy theory of higher categories
Hadrian Heine
Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this princi…