Blar i NTNU Open på forfatter "Haugseng, Rune"
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Free algebras through Day convolution
Chu, Hongyi; Haugseng, Rune (Peer reviewed; Journal article, 2022) -
Homotopy-coherent algebra via Segal conditions
Chu, Hongyi; Haugseng, Rune (Peer reviewed; Journal article, 2021)Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an “algebraic pattern”, by which we mean an ∞-category equipped with a factorization system and a collection of ... -
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
Haugseng, Rune; Hebestreit, Fabian; Linskens, Sil; Nuiten, Joost (Peer reviewed; Journal article, 2023) -
Monads, Algebras and Descent Theory Homotopy coherent version
Aslaksen, Even (Master thesis, 2023)Denne oppgaven utdyper artikkelen Homotopy Coherent Adjunctions and the Formal Theory of Monads av Emily Riehl og Dominic Verity, og begynner med å undersøke de grunnleggende konseptene i homotopikoherent kategoriteori ved ... -
On (co)ends in ∞-categories
Haugseng, Rune (Peer reviewed; Journal article, 2022)In this short note we prove that two definitions of (co)ends in ∞-categories, via twisted arrow ∞-categories and via ∞-categories of simplices, are equivalent. We also show that weighted (co)limits, which can be defined ... -
On distributivity in higher algebra I: The universal property of bispans
Elmanto, Elden; Haugseng, Rune (Peer reviewed; Journal article, 2023)Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of (∞-)categories of spans (or correspondences). In this paper, ... -
On lax transformations, adjunctions, and monads in (∞,2)-categories
Haugseng, Rune (Peer reviewed; Journal article, 2021)We use the basic expected properties of the Gray tensor product of (∞, 2)-categories to study (co)lax natural transformations. Using results of Riehl–Verity and Zaganidis we identify lax transformations between adjunctions ... -
∞-Operads as Analytic Monads
Gepner, David; Haugseng, Rune; Kock, Joachim (Peer reviewed; Journal article, 2022) -
∞ -Operads via symmetric sequences
Haugseng, Rune (Peer reviewed; Journal article, 2021)We construct a generalization of the Day convolution tensor product of presheaves that works for certain double \infty -categories. Using this construction, we obtain an \infty -categorical version of the well-known ... -
Segal Spaces in Homotopy Type Theory
Bakke, Fredrik (Master thesis, 2022)Homotopi type teori er et grunnleggende språk for å gjøre homotopi invariant matematikk, og dermed ville en forventet at det var et naturlig rammeverk å studere (∞,1)-kategorier i. Desverre er det for øyeblikket et åpent ... -
Segal spaces, spans, and semicategories
Haugseng, Rune (Peer reviewed; Journal article, 2021)We show that Segal spaces, and more generally category objects in an -category , can be identified with associative algebras in the double -category of spans in . We use this observation to prove that “having identities” ... -
Two-variable fibrations, factorisation systems and -categories of spans
Haugseng, Rune; Hebestreit, Fabian; Linskens, Sil; Nuiten, Joost (Peer reviewed; Journal article, 2023)We prove a universal property for ∞-categories of spans in the generality of Barwick’s adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts ... -
Verdier Duality for Stable ∞-categories
Sørli, Preben Hast (Master thesis, 2023)Vi beviser Luries ∞-kategoriske versjon av Verdier-dualitet. For å oppnå dette introduserer vi ∞-kategorier og noen viktige resultat og konstruksjoner. Mer spesifikt, så introduserer vi grenser og kogrenser og presenterer ...