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∞-Categories for the Working Mathematician
homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,Expand
Categorical Homotopy Theory
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 typically first encountersExpand
Homotopy coherent adjunctions and the formal theory of monads
In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterize its n-arrows using a graphical calculus that we develop here. TheExpand
Use of physician assistants as surgery/trauma house staff at an American College of Surgeons-verified Level II trauma center.
The Hurley Medical Center trauma surgeon/physician assistant model is a viable alternative for verified trauma centers unable to maintain a surgical residency program and consistency and quality of care indicated by shortened length of stay is a hallmark of such a model providing the highestquality of care. Expand
Homotopical resolutions associated to deformable adjunctions
Given an adjunction FaG connecting reasonable categories with weak equivalences, we define a new derived bar and cobar construction associated to the adjunction. This yields homotopical models of theExpand
The 2-category theory of quasi-categories
In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-category ofExpand
Six model structures for DG-modules over DGAs: model category theory in homological action
In Part 1, we describe six projective-type model structures on the category of dierential graded modules over a dierential graded algebra A over a commutative ring R. When R is a eld, the sixExpand
A laser includes a laser medium, a light source for emitting light which pumps the laser medium, a pair of mirrors which are disposed on opposite sides of the laser medium and form a resonator, anExpand
A type theory for synthetic ∞-categories
We propose foundations for a synthetic theory of $(\infty,1)$-categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it and use them toExpand