Category Theory | Fall 2026 · Math Club, ISI Bangalore

Table of Contents

CT2601: Introduction to Categories and Functors
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Speaker: Kinshuk Banik (B. Math, 2028)
Abstract: Natural transformations form the primary notion of maps between functors. We look at a bunch of motivating examples of natural transformations between some common functors. Obtaining the notion of mapping between them, we can start seeing functors as objects of some category, with morphisms being the natural transformations. This is the notion of a functor category. We end with a brief look at representable functors and natural transformations corresponding to them to make way for the Yoneda lemma.
Video: Available here
Date and Time: Saturday, 29th August 2026, 02:30 - 03:30 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Raushan Toor Nair (SMU)
Abstract: We prove the Yoneda lemma and use the lemma to give examples of natural transformations giving various morphisms between objects.
Video: Available here
Date and Time: Tuesday, 1st September 2026, 03:10 PM - 04:10 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Pragalbh Kumar Awasthi (M. Math, 2027)
Abstract: The talk will be an introduction to the notions of limits and colimts in the context of category theory. We will see how these definitions capture the idea of universality in a general sense and unify various useful constructions known to us in familiar specific categories. We will see examples where existence of certain limits and colimits can imply nontrivial results about the category, and at the same time realizing an object \(X\) as a limit or colimit can give valuable information about \(X\) and \(F(X)\) or vice versa provided \(F\) preserves or reflects certain limits. The general content requires no prerequisites, but for some examples, a background in algebra and topology will be assumed.
Video: Available here
Date and Time: Sunday, 13th September 2026, 05:30 PM - 07:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Balaji Subramonium (SMU)
Abstract: We shall introduce adjoint functors along with plenty of examples, and see how these interact with (co)limits. In the way of pre-requisites, we assume a passing familiarity with ideas introduced in the preceding talks and some basic algebra and topology (to follow the examples).
Video: Available here
Date and Time: Sunday, 20th September 2026, 04:30 PM - 06:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Kristaps John Balodis (University of Carleton)
Abstract: Given a (unital) ring \(R\), one can form its category \(R\)-\(\mathrm{Mod}\) of (left) \(R\)-modules. What properties of the underlying ring can be recovered from this category? We will begin to explore this question in this talk. Depending on pacing and audience feedback, possible results may include that module categories determine commutative rings up to isomorphism, recovering a ring from its category of modules, and the theory of Morita equivalences. A basic familiarity with rings, and with categories, such as natural transformations and products will be assumed.
Video: Available here
Date and Time: Saturday, 26th September 2026, 06:30 PM - 08:00 PM
Venue: Online

Speaker: Bhishek Garg (SMU)
Abstract: In this talk, we will see the definition of an abelian category and some examples. I will then talk about exact sequences and try to introduce homological algebra.
Video: Available here
Date and Time: Sunday, 27th September 2026, 04:30 PM - 06:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Boris Dhanjal (ICTS-TIFR)
Abstract: We will begin with a concrete question: Can one describe a space as a category? Higher categories will arise naturally as the structures that emerge from this question. We will cover topics leading up to operads and the recognition of loop spaces and \(A_\infty\) categories. Time permitting, we can also discuss homotopy categories and localization, then connect this picture with simplicial sets, Kan complexes, and quasi-categories. We assume familiarity with ordinary categories and basic topology.
Video: Available here
Date and Time: Tuesday, 13th October 2026, 05:00 PM - 06:30 PM
Venue: 2nd Floor Auditorium, Academic Building

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