48 citations · 167 across the 27 of their papers we have counts for
30 papers
A comparison of definitions of equivariant trees
Julia E. Bergner, Maxine E. Calle, David Chan +2
We show that various categories of trees can be modeled by Grothendieck constructions on categories of trees with a fixed set of leaves. We prove this result for the dendroidal cat…
Characterizing model structures on finite lattices
Kristen Mazur, Angélica M. Osorno, Constanze Roitzheim +3
Transfer systems on finite posets have recently been gaining traction as a key ingredient in equivariant homotopy theory. Additionally, they also naturally occur in the data of a m…
Realizing compatible pairs of transfer systems by combinatorial -operads
David Chan, Myungsin Cho, David Mehrle +4
We investigate how the notions of pairings of operads of May and compatible pairs of indexing systems of Blumberg--Hill relate via the correspondence between indexing systems and $…
Enumerating submonoids of finite commutative monoids
Caoilainn Kirkpatrick, Amelie el Mahmoud, Kyle Ormsby +6
Given a finite commutative monoid , we show that submonoids of - where is equipped with the max operation - may be enumerated via t…
Uniquely compatible transfer systems for cyclic groups of order
Kristen Mazur, Angelica M. Osorno, Constanze Roitzheim +3
Bi-incomplete Tambara functors over a group can be understood in terms of compatible pairs of -transfer systems. In the case of , Hill, Meng and Li gave a nece…
The symmetric monoidal 2-category of permutative categories
Nick Gurski, Niles Johnson, Angélica M. Osorno
We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetri…
Saturated and linear isometric transfer systems for cyclic groups of order
Usman Hafeez, Peter Marcus, Kyle Ormsby +1
Transfer systems are combinatorial objects which classify operads up to homotopy. By results of A. Blumberg and M. Hill, every transfer system associated to a linear iso…
Model structures on finite total orders
Scott Balchin, Kyle Ormsby, Angélica M. Osorno +1
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order , we enume…
Multiplicative equivariant -theory and the Barratt-Priddy-Quillen theorem
Bertrand J. Guillou, J. Peter May, Mona Merling +1
We prove a multiplicative version of the equivariant Barratt-Priddy-Quillen theorem, starting from the additive version proven in arXiv:1207.3459. The proof uses a multiplicative e…
Self-duality of the lattice of transfer systems via weak factorization systems
Evan E. Franchere, Kyle Ormsby, Angélica M Osorno +2
For a finite group , -transfer systems are combinatorial objects which encode the homotopy category of - operads, whose algebras in -spectra are $G…
2-categorical opfibrations, Quillen's Theorem B, and
Nick Gurski, Niles Johnson, Angélica M. Osorno
In this paper we show that the strict and lax pullbacks of a 2-categorical opfibration along an arbitrary 2-functor are homotopy equivalent. We give two applications. First, we sho…
Biased permutative equivariant categories
Kayleigh Bangs, Skye Binegar, Young Kim +4
For a finite group G, we introduce the complete suboperad of the categorical G-Barratt-Eccles operad . We prove that is not finitely generated, but is finite…
Comparison of Waldhausen constructions
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
In previous work, we develop a generalized Waldhausen -construction whose input is an augmented stable double Segal space and whose output is a unital 2-Segal space. H…
A multiplicative comparison of Waldhausen and Segal K-theory
Anna Marie Bohmann, Angélica Osorno
In this paper, we establish a multiplicative equivalence between two multiplicative algebraic -theory constructions, Elmendorf and Mandell's version of Segal's -theory and Bl…
2-Segal objects and the Waldhausen construction
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
In a previous paper, we showed that a discrete version of the -construction gives an equivalence of categories between unital 2-Segal sets and augmented stable double ca…
Symmetric monoidal G-categories and their strictification
Bertrand Guillou, J. Peter May, Mona Merling +1
We give an operadic definition of a genuine symmetric monoidal G-category, and we prove that its classifying space is a genuine E_\infty G-space. We do this by developing some very…
The edgewise subdivision criterion for 2-Segal objects
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
We show that the edgewise subdivision of a -Segal object is always a Segal object, and furthermore that this property characterizes -Segal objects.
The 2-dimensional stable homotopy hypothesis
Nick Gurski, Niles Johnson, Angélica M. Osorno
We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.
A symmetric monoidal and equivariant Segal infinite loop space machine
Bertrand Guillou, J. Peter May, Mona Merling +1
In [MMO] (arXiv:1704.03413), we reworked and generalized equivariant infinite loop space theory, which shows how to construct -spectra from -spaces with suitable structure. I…
Equivariant infinite loop space theory, the space level story
J. Peter May, Mona Merling, Angélica M. Osorno
We rework and generalize equivariant infinite loop space theory, which shows how to construct -spectra from -spaces with suitable structure. There is a classical version whic…
2-Segal sets and the Waldhausen construction
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
It is known by results of Dyckerhoff-Kapranov and of Gálvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove th…
Stable Postnikov data of Picard 2-categories
Nick Gurski, Niles Johnson, Angélica M. Osorno +1
Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category is an infinite loop space, t…
Extending homotopy theories across adjunctions
Nick Gurski, Niles Johnson, Angélica M. Osorno
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax…
K-theory for 2-categories
Nick Gurski, Niles Johnson, Angélica M. Osorno
We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of -objects in 2-categories. In…